You have included 4 weeks of holiday, but not sickness, training courses, conferences, company admin, next contract sales and worst of all bench time between contracts.
My calculation are you are down to 45 weeks after 5 weeks holiday and UK bank holidays. Add 5 days for illness, 7 days for courses and conferences, 1 day a month for admin, 3 days every 6 months for sales, and suddenly you are down to 39 weeks. Add at best 2 weeks of bench time as lining up new contracts perfectly is tricky and you are down to 37 weeks.
£350 * 5 * 37 = 64,750 before tax.
Then it is the whole consideration of whether you are within IR35, which basically taxes you more than a normal employee, and is very difficult to not be within if freelancing on longer contracts in the UK.
Then accounting, insurance, hardware costs etc.
You would have to be on some real long term contracts without benchtime, no illness, no training and no expenses to get towards you numbers.
Working in Shoreditch myself I know most of the decent developers with 10 experience around here are earning a lot more than a contract guy would make on £350 per day.