You can get time in a recording studio pretty cheap nowadays (As cheap as $15/hour). I have access to one I can use for free, and I know more than a few good people with good voices.
This would probably be significantly easier on TW than the mapping contest; all they'd have to do is have their sound engineer sit on his butt and listen to the submissions.
Part 1 of the contest would be a few test lines - perhaps chat lines from the game, as well as things that aren't chat lines from the game to see if submitters can get the
acting part of voice acting down. (For example, have a submitter say "I'm all out of ammo!" as if they were really in that bad of a situation and felt totally screwed, or have them quip "Looks like a back alley goth club in here!" as if they were extremely confident in themselves with a dash of black humor.) Men and women would be accepted.
After a good amount of candidates are chosen (maybe 50-100, 2/3rds men and 1/3rds women, since there's already 14 male characters and no female characters but this would allow for female characters to be created), TW would then present a full script for people to read out (i.e. every line that has to be said).
TW would then (quietly) select the winners and work with them to get the lines just right. Submitters handle the recording, TW handles the sound engineering and act coaching. Once they have these voices, this alone would make a worthy content patch and players would be very appreciative of it.
Simultaneously (and paired with this patch) would (hopefully) be an all-women DLC pack. (I'd pay more than $2.00 for it, tbh.) In relation to this, it would be nice if they modelled and voiced 6 females, put four in the pack and added two to the default roster (for a total of 8). This would stop that annoying thing on the character menu where there's always two blank spots at the end, and it would be fair to the new players who don't yet have the DLC but want to play a female. In the spirit of the original six characters, one of the freebie females should be a police officer and the other should be in the military.
Prizes, well... were there any prizes for the map competition? I don't know. A lot of people would do this just for the glory. I know I would, and I could probably convince at least half a dozen people to do it was well.
P.S. even though the game is British there are indeed people from other countries living in Britain. So not having a British/Irish/Scottish/Welsh accent should not be a *huge* problem (although I'm sure it would slant the odds of you winning in your favor a good deal). For all we know DJ Skully is Chinese.