What rate of pay should I expect?

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I'm going to email my manager for clarification but just out of interest what hourly rate should I expect to be paid in the following situation....

Week day rate is £10.50 ph
Weekend £11.50 ph
If I work a full extra shift I get paid and extra £1 per hour. This weekend I worked 2 full (8hr) extra shifts (totalling 16 hours) It was very last minute and I was reluctant to work this weekend so said to the person (not the manager) arranging cover I'd do it for double pay jokingly. They went off to speak to the manager and he said they would pay me time and a half. I agreed. I was told not to tell any other staff. So what rate should I expect to be paid per hour this weekend?

Normally if really short staffed (which we are) the manager gets in Agency staff but I think they charge around £22 an hour so I was definitely a cheaper option plus I know the role etc. The agency have let my work down on several occasions recently. I'm very reliable. Should I now expect time and a half each time I cover or was I being cheeky asking?

You were not cheeky asking, they could say no.

Time and a half is likely to be £10.50 x 1.5 = £15.75 as the £11.50 and extra £1 per hour are premium rates for weekend working and full extra shift. The time and a half is a premium rate so starting point is base hourly rate.

Whilst Agency staff cost £22 per hour that will include holiday pay and other elements. It may also include agency fee. Also your hourly rate is not the full cost to your employer I.e. you accrue holiday, have employer NI, possibly employer pension etc.

WRT future weekends, it sounds like a one off as they really needed you to work. They cannot continue to pay you time and a half and not pay other staff the same. The pay policy you have quoted seems fairly standard to me for organisations that work 7 days a week, it would require an organisation wide change from £11.50 per hour plus £1 hour for a full shift to time and a half (of £10.50) which would be very expensive for the employer with increased NI and pension costs.

I'd expect £11.50x1.5 = £17.25x16 = £276 for the weekend.

I would not expect both weekend enhancements. I would interpret this as you negotiating up from the usual extra £1ph enhancement to time and a half. So £10.50 x 1.5.

I think what agency workers get is irrelevant.

I would translate that as time being your basic hourly rate of £10.50 plus half £5.25. So £15.75ph 😊