I’m with Atilla - you’re not going to get a straight answer.
I know not all men are the same, but I’ll share my experience.
I also got given the excuses - “my friend sent that email as a joke!”
(your friend who never comes round, used your laptop that never leaves the house... ah, it had virus so you dropped it off with him... but you’ve already named the friend in the first part of the excuse and he knows fuck all about computers... and, bottom line - it’s just not even funny. There’s no joke there. Anyway - so, I got the crap excuses too!)
As an aside: men who have used prostitutes always seem to have friends who send joke texts to prostitutes, don’t they? I’ve seen variations on this on here before. And yet, of all the men I’ve ever dated, the only one whose mates have found it funny to do this - was the one who was later proved to be a liar who had used prostitutes. Bottom line: men do not send messages to prostitutes from their mate’s phone as a joke. They just don’t. It’s not funny.
Back to my experience...
Like you, I needed the truth. I told him - in front of a counsellor to prove I was genuine - that I believed he was lying but with the truth (admitting he’d done it) I would not leave him. I meant this. He lied. “I never went through with it”.
Later, I promised the same thing, that I wouldn’t leave - that time I was lying trying to get the truth. Still lied.
All the while I became someone I hated, snooping, trying to find evidence. I would find stuff and be so pleased when I backed him into a corner - like you and the missing £90. But honestly, I was just trying to restore my pride “ha, you can’t fool me, I’m not that stupid - look! I got the evidence” (or I can slay your pathetic excuse - like a phone shop being 3 hours away...) I was just trying to make myself feel better. He was making a fool of me, because I was still there.
Then one day I found numbers dialled to a prostitute on an old phone.
This time he again said “I never went through with it”.
Only this time was different. TBH, other things had moved on. I was desperate for a sexual relationship again (he disgusted me and I was fearful of STIs, we hadn’t had sex in a long time). We’d recently been able to increase our savings, so there was money for one of us to move out. My newborn wasn’t newborn any more and I’d managed to get some SLEEP. A few other things. I was in a different place.
Finally, instead of searching for evidence to trip him up, needing the truth from him, it went like this:
- this phone shows me the prostitutes you called
- I never went through with it
- you did, but even if you didn’t - don’t you see that that would be enough? We are over, I am divorcing you
I was so fucking relieved!!!!
I was just set free from caring about evidence.
I knew what he had done. I didn’t have to prove it. The law is great like that!
I didn’t have to sneak around trying to see his phone, trying to guess his email password.
To this day, he has never admitted it to me. He got careless (or just didn’t care) after we split and I saw the evidence. Plus neighbour told me about his house calls when I was away 
You know what he did. You don’t need to demean yourself looking for evidence. This is not a court of law where you have to believe his obvious tripe until you have evidence beyond reasonable doubt.
It look me a long time to reach this point - but I felt so free, the day I realised that I didn’t need to prove a damn fucking thing.
Good luck to you 