You should certainly give them a ring, I don't see why they shouldn't be able to move you over to an ADSL 2+ service, this could double or even almost tripple your speeds. Going by what you get now you must be fairly close to the exchange.
If they won't move you over without locking you into a new contract you may want to consider moving to a ISP who does monthly contracts such as Plus Net, with prices starting at £6.49 a month.
Yes you will need a new router, I had to retire my trusty DG834 V1 when I moved over to ADSL2+. They are supposed to be compatible, but I had no end of problems, in the end I used my brother V4 version, they are supposed to be the best of the 834 range and can be picked up on ebay pretty cheaply (about £20)
Another tip, some ISPs cap your upload speed, this is the case with Plus Net but you can simply raise a support ticket asking for it to be uncapped, they may tell you it'll affect download speed, but it won't.