Crazyface
Tour Winner
We own the freehold to the property next door to us. Do we have any magic powers we can exert on them? 
Sell them the freehold
Look at your leasehold agreement, all the answers are there.
Don't know if we have one. When we bought the place the solicitor just said "oh and you own the freehold for next door as well"
As the solicitor gave you this information he must have read it somewhere, so even if your house and next door are not registered it it must be part of the title deeds so read them. If you have a mortgage the title deeds will be lodged with the mortgage company or their appointed solicitor for all the legal work during the conveyancing.
It is very easy to check with the land Registry to see if both properties are registered. However they may not hold all the paperwork (they do not for mine as I have got it).
If not registered you can do it but you will have to pay a 1st registration charge.
If your neighbour has an original 999 year lease (quite common) you may well consider selling it to them.
My last leasehold property only gave the the landlord a ground rent of £30 a year so he kept trying to sell the freehold to me.