Transpact.com is Europe's leading Escrow service.
They provide world-beating protection, and are highly recommended.
As BrunoPuntzJones has pointed out, you must independently check on the UK Government's FSA agency online register that Transpact.com is authorised and regulated and genuine (which they are).
You cannot get more genuine than Transpact.com.
The reason they ask for your bank account details is because, as an escrow service, they may well have to make payment to you, and they cannot pay you without knowing your bank account details.
As a financial company, they are also mandated by law to 'know their customer', and that is why they confidentially ask for your date of birth and other information (they would rather not have to do this, but the law gives them no choice).
I don't know if you are buying or selling, but the key to Transpact.com is to ensure that the conditions you set and agree to cover you in every eventuality:
If they do then as a buyer you are guaranteed to get everything you were promised from the seller or your money back (one heck of a guarantee).
If they do as a seller then you are guaranteed to get paid 100% in full.
[Declaration - I work for Transpact.com - but it is a great company]
The UK's FSA (Financial Services Authority) is roughly equivalent to the USA's Department of Treasury and/or SEC (Security and Exchange Commission)