wife left matrimonial home should I pay?

Yes paying cash is asking for trouble. Lawyer thrive on ambiguities and exploit them to cause conflict and prolong legal hearing and subsequently get paid more. The legal proceedings are basically one big pitty party and whoever story of woe is better the more they are rewarded, my own ended up like an episode of Eastenders. So she could go into court saying you are such a bad guy because you haven't paid any child support, you will say I did I paid cash, where is the proof. I've even read on here one person who paid child support voluntarily by bank account transfer and their ex claimed in court he didn't and the payments were repayments for some debt.

So the calculator is here

www.gov.uk/calculate-your-child-maintenance

These are fixed calculations and the only way a court will get involved is on a temporary order basis until the CMS have done a calculation or if you are earning megga bucks, in the hundreds of thousands.

I pay voluntarily by bank transfer but depending on how your ex is you may decide it's worth the £100 or so to pay the CMS do an official calculation and remove any ambiguity.