Welcome to LB Sarah, you must be knew around here? 
The standard responses you’ve received to what is a perfectly reasonable question, regardless of how feasible or otherwise, are what you’ll come to expect over your time with LB. Negative, derisory and generally toned in the ‘what the feck are you on about’ style are regular and standard responses from the people of LB, maybe we should alter the site name to London ‘Daily Mail’ Bikers? 
My two penneth, it’s a reasonable point to make, why shouldn’t local users of a service, regardless of this service being provided privately, ask for a better quality of experience when using the service? The council, as you’ve already mentioned, govern planning and alterations to the delivery and use of the service therefore would need to be approached as well as the service provider themselves.
I suspect those that run the tea hut would love to improve the seating and shelter arrangements as it would no doubt bring in more custom, and if we as users of this service are willing to assist in improving these arrangements for ours and others benefit then why not? Are we so selfish that we’d only do this solely for our benefit?
In principal I think it’s reasonable to make further enquiries, although the practicalities of any changes happening are a different matter.
The only thing I will say is that the ‘Friends of the Heath’, in essence the vocal NIMBY residents, have in the past put pressure on the council re: reducing the parking provison by the tea hut. I believe if they had their way it would be gone altogether.
They think it detracts from the overall appearance of the heath, read: devalues their property, and they don’t like the fact that it, in their eyes, attracts the less savoury members of society, cabbies, bikers, truck drivers, people on their way home from the pub, in essence anyone that’s not them!
