Why not? You can sell anything you like for what price you like.
A future buyer knowing a house was sold for £1 would have searches
on the house anyway, so no problem in the future.

There are all sorts of laws about selling property below market rates.
Inheritance tax implications, for example, and state payment of care fees
where they believe assets have been disposed of to validate a claim. It
would also be easy to find ways of avoiding tax by using suspicious
disposals of property.

If you sold a house to someone for £1 and they gave you a gift of £200,000
the next month, you'd probably end up in prison, so it isn't possible to
just give stuff away, especially if there is some implied contract.

On the inheritance tax side, if the daughter pays £35,000 for a house worth
£200,000 and her parent/s dies within 7 years, she may have to pay some
inheritance tax on the difference.

Paying £35,000 WILL attract the attention of the taxation authorities, so it
probably does require the services of an accountant to smooth the passage.
It may be better to notify the authorities of the deal, letting them know it
is basically a gift from parent to daughter. I have no idea if stamp duty is
on the sale price or the value of the property, if this is much lower than
the sale price. I'm sure an accountant or solicitor can advise.

Christian.