Where is your manager in all this? You have the form, is he/she refusing to do the assessment with you? When you raised your specific concerns with your manager what did he/she say?
Yes your employer are obliged to complete a risk assessment for you, and you could make a complaint to the Health and Safety Executive but really I think the better thing to do at present is to work out the most effective way of dealing with the risks you've identified.
I don't think problems clients and a heavy workload are health and safety issues. They are things you need to raise with your manager directly not put on a health and safety form for HR.
In terms of the heat, what is there that could be done? I'm trying to get at what you think would be achieved by someone filling in a RA form that couldn't otherwise be achieved. I'm assuming opening a window or turning down the heating/up the A/C are all not possible? What about a desk fan? What sort of thing have you asked your manager to do about the heat that is not being done?
If you feel sitting down all day is a risk to you, I think that's something you and your manager could resolve quite easily, with you taking regular walks round the office to stretch your legs or something. Again, what have you tried to do to sort this out that hasn't been done and you feel will be done if a form is filled in?
At the end of the day if your employer refuses to do a risk assessment for you or refuses to deal with risks identified, they are breaking the law and you can make a complaint. But the risks you've identified don't require a massive change in your job or anything like that. You are not being asked to lift heavy loads all day, or work with dangerous substances or whatever. You are too hot and need to stretch your legs. So although your employer is wrong by not doing one, and your concerns are valid, in this instance I think your best option is to do what is most likely to get the risks dealt with, which is you sorting things out yourself.