My house, which is in England, is immediately adjacent to a plot of
land for which ownership is unknown - all searches and enquiries have
yielded no result. I want to buy this plot of land, or at least
establish a right of way and use. Is this possible, and if so, how?

Hello Annadrew

You have not stated who you have enquired with to discover who owns
the land next to your property but hopefully I can help you do this.

In the UK The Land Registry (LR) is the body that holds records of
land ownership.  The LR have a website at http://www.landreg.gov.uk
which contains numerous documents and a vast resource of advice.  In
2002 the the Land Registration Act was passed to simplify, improve and
modernise the current laws.

The details of this can be found here:
http://www.landreg.gov.uk/legislation/lract2002/default.asp

The LR has a number of fact sheets that cover the changes in the act
available and the practice guides provide detailed guidance of what
you can do to register the land next to your property.  These can all
be downloaded from the website or ordered on CDROM.

http://www.landreg.gov.uk/legislation/lract2002/default.asp?pkey=385
http://www.landreg.gov.uk/legislation/publications_sm.asp?pubtype=35
http://www.landreg.gov.uk/legislation/publications_sm.asp?pubtype=36

In your case, I have looked at the Boundary Questions factsheet and it
advises that if you contact the LR they may be able to tell you who
has registered the land next door to your property and other relevant
details from previous owners of the property.

This factsheet is PG006 on this page:
http://www.landreg.gov.uk/publications/default.asp?pubtype=16

This factsheet also briefly discusses the law of Adverse Possession
which entitles you to put a claim to the land.  The factsheet states
that this is a complex area of the law where you should contact your
solicitor or legal advisor.  If you apply to the LR and they believe
you have an arguable claim over the land they will serve notice on the
existing land owners for you.  This could of course lead to a dispute
and possible costly court proceedings (should it go that far).

The factsheet also discusses "Alternative Dispute Resolution" methods
which basically mean that the LR will put you in contact with the land
owners so that an amicable changeover of the land can be discussed. 
This would be especially useful for you should you wish to only
establish a right of way (rather than outright ownership).

The contact details for the Land Registry given at the end of this document are:

Land Registry
32 Lincoln's Inn Fields
LONDON
WC2A 3PH

Useful Factsheets:
LRFS015 http://www.landreg.gov.uk/legislation/publications_sm.asp?pubtype=36
Discusses the various search methods that can be employed on the land.

LRFS002 http://www.landreg.gov.uk/legislation/publications_sm.asp?pubtype=36
LRPG004 http://www.landreg.gov.uk/legislation/publications_sm.asp?pubtype=35
LRPG005 http://www.landreg.gov.uk/legislation/publications_sm.asp?pubtype=35
Discusses Adverse Possession and particularly interesting to you will
be third one relating to Adverse Possession of unregistered land.

I hope this summary of the Land Registry is helpful.  My advice would
be to contact the LR for their action pack.  Contact the LR and ask
them for the details regarding ownership of the land next to your
property and to ask for adviec regarding possession should this land
be vacant.  Finally, this area of the law is extremely complicated and
complex so you should contact your solicitor or your local Citizens
Advice Bureau for full legal advice on this matter.

Should you require any further information please ask for
clarification and I will do all I can to help.

Easy!

Just fence it off and if, after 10 years, no one complains ... It's Yours!

Congratulations.

CORRECTION: 

It's 12 years and it's known as: 

'Adverse Possession'  
The acquisition of title to property through possession without the
owner's consent for a certain period of time.

'Adverse Possessory Title'
If a piece of land is occupied without permission for at least 12
years, the occupier can become the legal owner.

Here's an Essay that refers:

http://free-law-books.troy.rollo.name/possession.pdf

It's your lucky day!

You also asked about establishing a 'Right of Way'.

If folk already have a Right of Way, they may well object to your
fencing off some or all of the plot.

So, 'Rights of Way' are often a matter of fact.

They can be reinforced by signs that proclaim 'This is a Right of Way'.

However, that may be counter-productive if you want the plot for yourself.

I know several folk (including my next-door neighbour) who have just
fenced off a lump of adjoining land and Hey Presto!

A critical component is that you should 'maintain' the plot that you
have fenced off ... by repairing the fence, maybe cutting the grass,
sprinkling weed killer around, tidying up rubbish, etc.

In other words, looking after it as if it were yours.

The trick is to treat it as if it IS yours and, in practice, most
people will naturally assume that it is.

I wouldn't use a lawyer if I were you, I would just do it. This is an
old Common Law right.

The fencing does not have to be expensive. Just a few posts with two
or three strands of wire should do the trick. It will be LOTS cheaper
than going to a lawyer who may inadvertently alert people to what you
intend doing.

And THAT could be expensive and self-defeating.

Best of Luck!