It would depend entirely on your works pension as to whether they accept contirbutions from another savings plan. You'd have to ask your works pensions administrators. What's DC?
I doubt it. I pay AVCs alongside my regular final salary pension and the two are completely separate. I can`t access either until I get to my nominated retirement date. I would think that because your pension contributions are taken out of your salary before tax and so are your AVCs then you can`t combine the two.
I transferred my AVC's into my workplace final salary pension scheme when I took my pension. It worked out as a better deal than any external pension provider could pay.