Way back (in internet time) when we took a look at an alternative to your state issued passport. Lets look again at it:

THE
WORLD
PASSPORT

The World Passport is a 30 page document printed in 7 languages: English, French, Spanish, Russian, Arabic, Chinese and Esperanto. Each passport is numbered and each page contains the World Citizen logo as background. Two pages are reserved for affiliate identifications: diplomatic corps, organizations, firms, etc. There are nineteen visa pages. In the inside back cover, there is space for home address, next of kin, doctor, employer, driving license no. and national passport/identity number. The cover is blue with gold lettering.Go to World Passport Application Form

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The World Passport represents the inalienable human right of freedom of travel on planet Earth. Therefore it is premised on the fundamental oneness or unity of the human community.In modern times, the passport has become a symbol of national sovereignty and control by each nation-state. That control works both for citizens within a nation and all others outside. All nations thus collude in the system of control of travel rather than its freedom. If freedom of travel is one of the essential marks of the liberated human being, as stated in the Universal Declaration of Human Rights, then the very acceptance of a national passport is the mark of the slave, serf or subject. The World Passport is therefore a meaningful symbol and sometimes powerful tool for the implementation of the fundamental human right of freedom of travel. By its very existence it challenges the exclusive assumption of sovereignty of the nation-state system. It is designed however to conform to nation-state requirements for travel documents. It does not, however, indicate the nationality of its bearer, only his/her birthplace. It is therefore a neutral, apolitical document of identity and potential travel document.A passport gains credibility only by its acceptance by authorities other than the issuing agent. The World Passport in this respect has a track record of over 50 years acceptance since it was first issued. Today over 150 countries have visaed it on a case-by-case basis. In short, the World Passport represents the one world we all live in and on. No one has the right to tell you you can’t move freely on your natural birthplace! So don’t leave home without one! […]

http://www.worldgovernment.org/docpass.html

So, you can get one of these passports, and then keep it and your expired British passport together when you travel. You leave the UK on your Expired British passport, enter your destination on your World Wassport, and then re-enter the UK on your expired British passport, since they cannot refuse you entry to Britain just because your passport is expired.

OR can they?

Is there a rule saying that you cannot leave the UK on an expired British passport? I know people who have left the UK on expired foreign passports (and then even entered the countries that they were going to on expired passports), so we would have to google that.

Then there is the possibility of getting a passport from another nation. It is presumed that this is harder to do, since normally you have to be a citizen of a country to get its passport. A quick google throws up:

How You Can Have a Second Passport, New Residency & Global Freedom
By Catherine Jones.

Why deal with one nation on its terms; when you can deal with all nations on your terms?

As things continue to deteriorate inside the United States
having a second passport becomes more and more of a priority
The loss of civil liberties in the USA has become chronic – the growing censorship, a stark warning.
Rational people having taken notice – those with their heads in the sand must bury them deeper to block out the obvious.

A new e-book by Catherine Jones – This is the only e-book that will get you a second passport; without the hype, the rip off, the B.S. and the run-around common to most books on this subject. This e-book will also show you how to get residency, work permits, retirement residency, and student visas in every region of the world. Twenty seven nations covered – 241 pages of rock solid facts.

How Do We Get A Second Passport?
This e-book supplies the answers, the methods and the requirements, (the majority of which are not commonly known,) for getting a second passport. This e-book can get you into the EU. This e-book can help you retire in dozens of nations. This e-book covers the subject of gaining legal residency, a second passport, work permits, asylum, honorary passports, retirement visas, and a great deal more, it provides the real facts and the real solutions, which sets this e-book apart from anything else in its category. This is neither a dream book, nor a book about vague ” under the table ” deals; it is an e-book about what it takes to get new residency, a second citizenship and a legal second passport. In fact.

The information complied by the author has never before existed in a unified form. This e-book is a first. The data was all but impossible to compile, even on a case by case basis, as for the most part none of it was posted or publicly available. It had to be extracted, like an elephant’s molar, from each separate government, and then the precise agency within that government, always at great effort; and only after the correct government agency could be found. The immigration offices, their systems and their requirements for conveying information differed absolutely in every nation that was contacted. It was like trying to find a needle in an infinite number of haystacks. […]

http://www.escapeartist.com/

and this, from a firm of specialst lawyers:

Henley & Partners are recognised as the world’s leading specialists for exclusive private residence solutions. We have also built an international reputation for citizenship law of selected countries, comparative citizenship law and the acquisition of alternative citizenship. We advise on all legal possibilities and programmes currently available to acquire an alternative citizenship and to legally obtain a second passport. We give unbiased information and advice on the advantages and disadvantages of the available options. Individual clients as well as other law and consulting firms worldwide rely on us for specialised advice and assistance in this delicate area where our expertise and experience are second to none.

Alternative Citizenship and a Second Passport – Freedom to Travel and to do Business, and Security for Life.

Citizenship and Passports

Citizenship is the relationship between an individual and a sovereign State, defined by the law of that State and with corresponding duties and rights. A passport is a personal identification and travel document for international use issued by a sovereign State. Generally, only passports which are issued based on a person’s citizenship are of any interest and use. Only through the acquisition of full citizenship can you legally acquire the right to a passport. Non-citizen passports and other passports issued to Non-citizen passports and other passports issued to non-citizens are most of the time illegal and/or useless, with certain exceptions such as the Panamanian non-citizens passport issued to persons holding a retiree residence permit in Panama, or diplomatic passports issued to non-citizens, UN and refugee passports and certain other travel documents issued by international organisations or individual States. Diplomatic passports are only legal and useful if issued by the competent authorities within the issuing State or international organisation and if the holder is properly accredited in the receiving State.[…]

http://www.henleyglobal.com/m-citizenship.html