Also, the landlord is the letting agents client so they should be paying.
It depends on the agent, often the LL is paying too. The agency I work for charges the majority of the fee to the LL and a small (by comparison) fee to the T. The idea of requiring the T to pay a fee for referencing and the agreement is to avoid them pulling out at the 11th hour after all of the work has been done - which is really common.
I agree that renewal fees shouldn't be charged. We don't charge them, the tenancy goes periodic after the fixed term (unless the T requests otherwise).
I agree that it is expensive to rent, but in the defence of the less scrupulous agents, lettings take a lot of time and can often be loss leaders, despite the fees seeming expensive.
The trouble is there is so much difference from agent to agent and greedy agents give the good ones a bad reputation. It's the same with deposits, the majority of tenants will be excellent and a months' deposit is refunded without dispute. Unfortunately there are others that leave properties in such poor condition that 1 months' rent doesn't touch the sides.
We base our fees on a percentage of the rent, which in theory should make the fees appropriate whether you are renting a flat for £500 pcm or a large house for £3,000 pcm.