Upvote:3
The accesrail site lists IATA airport codes for the train stations. I've tried putting those into flight-search engines and even the sites belonging to the airlines that accesrail mentions as participating, and they don't recognise them, so I think the only answer is to use a travel agent.
Note that the airport codes do not match the UK rail station codes, e.g. Bristol Temple Meads is BRI on UK rail, but TPB on IATA - if you put BRI into a flight-search engine, you'll end up in Bari.