I severely doubt this is correct. Customs in London doesn't care where you're going, they just care whether you're carrying contraband or dutiable goods above the allowance.

To the OP: if you have proof of enough funds to buy a ticket out, most countries will accept that. It's worth bearing in mind that some, but not all, of Europe is part of the Schengen agreement which is basically a universal immigration and customs area. If you are asked for proof of a departing booking by such a country, they mean your departure from Schengen and not from that particular country. A major credit card would be fine; you can always tell them that you're planning to depart by Eurostar to London, and if you are seriously worried then book yourself a refundable Eurostar ticket before you go which should only cost a few hundred euro.

The country you enter may also be interested in establishing that you have enough money to support yourself during your visit, so you should bring proof that you have the money in your bank account, or cash, or a credit card showing an appropriate limit, or some combination of the above.

Also remember that while there's a limit of 90 days in Schengen per 180 days for US and many other passport holders, places like Ireland and the United Kingdom aren't in Schengen so don't count towards that limit.