Here's what you do.. Divide �184.70 by 1.22. This gives you �151.39 - that's the pre-tax amount. Obviously, if your tax rate was, for example, 26% then you'd divide �184.70 by 1.26.
Regardless of the correctness or otherwise of the arithmetic above, there is an error in the assumption. Your marginal tax rate may be 22%, but you only pay this on part of your income - you will get a proportion of your annual personal tax allowance and a proportion of your annual 10% tax allowance before you start paying 22%.
So as an arithmetical exercise, fine - in the real world no.