As far as I know:
If it is a loan, then potential tax consequences are only on the lenders (parents in US) and only in US.
If parties agree on market rate interest, then parents should pay US tax on that interest.
If it is the interest free loan, AND lenders (children) have no investment income, then US exempts lenders of tax for up to $100,000 loan. (Which in practice could mean up to 400K, if there are two borrowers and two lenders.)
Otherwise, lenders pay tax on "deemed" interest (equal to the market rate).
And there is no formal requirement of lending agreement done by solicitor.
If however it is a gift, again there are no UK tax consequences (since gift givers are not connected to UK), but lenders have to file form 709, gift report, to IRS, and it will count towards their lifetime allowance, which is now about 13 mln per person.
But in either case, when buying a place, solicitors would demand detailed proofs of where funds proceed from.
Also, we transferred sums of the order of 200K and more using Wise and/or Interactive Broker before and no questions were asked. But it is always the best to have all paperwork ready on where the funds come from, just in case.