I think you should proceed with the offer you originally accepted. We were on the other end of this recently - house on market for 4 days when we viewed it on a Saturday, the missus loved it (I liked it too). The vendor was showing us round and said there was an offer but she hadn't spoken to the agent yet so no details (not that we expected her to share them with us).
We second viewed first thing Monday and offered after that, full asking which was the top of our budget. Agent said one other had offered asking also so she'd put it to the vendor and get back to us for full and finals. I said that was our full and final, vendor went with the other buyer as they'd apparently offered first.
Two days later the missus decided we should have offered more and wanted to go back with a higher offer. We could only have gone a grand or two higher and it didn't sit right with me anyway so I said no.
Upshot - if they'd have accepted our offer and then come back to say they'd taken another higher offer we'd have been mightily peeved and wouldn't have dealt with them if they'd come back later.
Buyer B bluffed and it was called, if they've come back afterwards with another £10k I'd be very wary, who's to say they won't try and knock you back down after surveys? Bad form IMO, but that could be why we're still looking for a house!
Personally I think in our case there was more to the decision than who offered first, we're in no chain, everything ready to go, said we could complete in 6 weeks all being well. I did however tell the agent that since we had everyone lined up we didn't need to see their IFA or speak to their conveyancing firm. The agent tried to hard sell me and when I asked if that would affect our offer she said no, but she couldn't say wether or not the vendor might feel differently(!).