When a company trades as a different name to their legal name (e.g. Fred Bloggs Paving Ltd. t/a Crazy Paving). Is it legal to raise invoices using their trading name only?

The situation you describe is covered by the disclosure rules of the Business Names Act and Companies Act legislation. This says that you must display the company’s identity and address where documents can be served on all letterheads, invoices, orders etc as well at all trading addresses. So in your case, assume that you put on the heading of the invoice the trading address:

Crazy Paving, Unit 2, New Trading Estate, Barchester, Barset, BA33 4ET

Somewhere on the invoice you must also have the address where documents can be legally served. So it could be, for example:

Fred Bloggs Paving Limited, registered in England & Wales. Registration number 1234567. Registered Office: 5 Middle Street, Barchester, Barset, BA4 5QR.

In this example Crazy Paving is the trade name of Fred Bloggs Paving Limited and the company’s trading premises are at the Trading Estate but the registered office is the address in Middle Street.