Most councils are cashstrapped these days having to find money for nursing homes etc. They have probably been looking to see where they can get extra money from.
Who owns the grass area? If the cafe own it they might still need permission to put chairs there - I don't know the law on this, but I din't see why they would have to pay an annual fee.
If the council owns it then the cafe is, in effect, leasing it so it is not unreadonable for the council to charge. If the cafe is allowed to do it, what is to stop all and subdry setting up a business on common land - verges, parks etc?
However, even if the Cafe does not own the land, but has been cutting the grass and generally using it gor many years they may have established a right to it. This would have to be looked into by a splocitor or someone who knows more about it.
Assuming the cafe uses the outside space for six months of the year and is open every day, the cost works out to about £11 per day. Depending on how many customers they get, that could be an extra 50p or so on each bill. If this is going to put them out of business they will have to stick to staying inside or try to negotiate a reduction in the charge.