Independent coffee shops and cafes might be a little bit riskier when it comes to coffee quality, but if they look as traditional as the Market Coffee House then have a bit of faith and try them out. In this case you'll be very plesantly surprised.
All the old dark wood panelling and the tiny tables up to the bar - that would be more in place in a pub – make walking into this coffee house a bit like walking back in time into the coffee houses of 18th Century London. This is a big statement to make seeing as I've never been into one of those coffee houses, but it's certainly how I imagine it would be – but with cleaner windows and less smoke.
It's not just a house of coffee, tea, hot chocolate and the like either, they also serve wine etc. And food. In fact more than half of the space is a restaurant, serving gamey ye olde English type food from a small menu. They also do breakfasts and afternoon teas – the traditional kinds of both.
And don't worry, the coffee is as good as you'd hope it to be.