Things to consider:
1) How are you going to access the areas internally? - Most leisure centres own a scissor lift so perhaps approach them, the stair well would by the looks of it would have to be platformed, you just can't stand on the ledge and expect H&S to approve that method?
2) There is no hard and fast pricing structure to stick to on this. remember, most of these type of establishments have very limited budgets, speak to the manager and ask how often they get the windows cleaned, ask him why he is looking for other quotes (some org's have to submit 3 quotes by tender under the legislation of council contracting), ask him what is his main issues are regarding the cleaning, price, H&S, standards, ALL windows cleaned each visit?
3) When you have a better understanding what is involved and what the key factors are then you can think about putting together a proposal. If H&S is the main issue then push this at the forefront of your quotation, likewise with Standards, Reliability, whatever is his main concern cover this first and highlight your ability to deliver results!
4) Work out the time it will take you to do the job then base your hourly rate on this and work with these figures. DON'T be greedy, these jobs are guaranteed all weather work, but likewise don't sell yourself short!
5) Council contracts generally need a chase up for prompt payment so bear that in mind?
Hope this helps,
Regards,
Trevor