Different departments have different discounts. If you speak to the tech team or to the customer service team or to the TV help team, you should not expect them to offer you a massive discount for the TV subscription, as that is not what they are primarily there to do.
The discounts are not the same because the system generates them based on account history - I've mentioned it before, it takes everything into account, for example payment history, offer history, bill history, tenure, even the postcode. If you've been with the company for a while but have been on massive discounts because you play the system, then the system will generate some better discounts to ensure it can match what you're after, but even the system can only discount the subscription up to the point that it decides it is no longer profitable - that is why offers always change and people tell you they are point of call, because once the system refreshes overnight it will generate new offers or remove offers from an account based on what has happened and also how likely a customer is to accept them (based on number of times the customer has phoned in).
The rule of thumb is that for discounts, if you're an active customer, you need to speak to Retentions. If you speak to them twice or so, and still feel it's not enough, then you can cancel and speak to Winback a few days after, to see what's available to reinstate the account. If not even Winback can offer you a price you are happy with, then Sky are probably not the right company for you at the particular point in time, and you may want to consider joining them again in the future.
Another rule of thumb, is that if you're offered a price close to what you were paying before (within say £3-4) then that is most likely the best you can get. It's really rare for the subscription to be cheaper when you recontract because in the meantime there has probably been at least one price increase and one offer change. If you still feel that it's too much, then you may want to cancel and speak to Winback, but really if you don't value the subscription at that price, it may be time to cancel.
The offers you've been quoted are the best you can currently get from Retentions. Cinema is normally £10, and Entertainment was £22 up until a week ago but the department has had some trouble with save rate recently, so that changed again to £20 to gauge whether it makes a difference or not. The admin fees cannot be removed, as it is a business decision for them to be there.
I just did it because I was curious.