For £10k I would bank transfer, before faster payments days you had to go in branch and pay a fee. Now it is much quicker, easier and free. You just need to transfer online or via telephone banking and it will be in the seller's account within an hour (normally instant)
Cash is good for smaller amounts but count it in front of the seller.
If it is a dealer at least £100 on credit card, if possible, so you get section 75 protection.
Going to the local bank branch with a private seller and either handing over the cash or doing a transfer sounds good but logistically it is a bit of a pain because not everybody has a bank just down the road. It sounds like something you would do if you didn't trust the seller/buyer.