Running costs low as you say and from the existing BBC Music budget. BBC local radio budget and how it is allocated is not relevant.

Bob Harris also sent in comments to Ofcom:

"My work since the early 1970's on radio and television has helped contribute to what we know to be a stunning sound archive unique to the BBC. This amazing treasure trove of music, interviews and sessions would almost certainly be the backbone of the Radio 2 Xtra output and I am absolutely certain that the broadcasting of this material would genuinely enhance the lives of our listeners without threatening any existing services.
Our audience has always supported the work of the BBC through levy of the license fee and this is surely a wonderful opportunity to reward their loyalty by offering access to the carefully curated programmes and unique material that Radio 2 Xtra would offer. It doesn't make sense to me to deny the listeners this opportunity."

The BBC altered their proposals to increase their use of archive material, increase the speech element of those programmes and broadcast them during the day when radio listening is at it's peak. They also said that these programmes would repeated several times.

BBC4 is showing lots of archive music programmes, with some new commissions, as well as performances from their TV shows on Fridays. Some from Wogan which I never watched. I don't see why BBC radio should not do the same. They could do this and not just concentrate on the 50s, 60s and 70s, a music led version of Radio 4 Extra.