returning to the country he is applying for asylum from would pretty much invalidate his claim.
travelling to other countries is something which is not looked on favourably as there are issues with where the funding came from (vast majority do not have permission to work) and could almost be seek as an attempt to stop people cherry picking which country they claim asylum in.
'travel documents' (passports for people with some limited status such as refugee status or indefinate leave to remain) are only issued to people who are legally allowed to reside in the country therefore asylum seekers can't apply. even once you get a travel document you cant return to your original country without risking having your status reconsidered.
most asylum seekers who have been here for years (if not decades) now have had their claims passed to the legacy teams at the home office who are working through a pretty hefty backlog of claims deciding who gets status and who doesnt. there is a target to get these completed by 2011 but who knows...
using a legal rep to make some form of submissions to the home office to make a claim be looked at sooner is possible. however if no new information or evidence is available (since there are a decent percentage of failed asylum seekers who have made fresh claims) then there may be no new decision made.
immigration advisory service offer a few different services which may be of use.
http://www.iasuk.org/home.aspx or try a local cab or law centre if any are nearby.
just be weary of smaller immigration solicitors, some are fantastic, some are dire...just dont go with the first one you find, as with anything just shop around.