Good grief, yet another one....
I hope you've read some other threads like this in recent days, singlediva and gained some comfort that you are not alone. But you will have also seen that when this happens, there is a script.
It goes like this.
H says I love you, but I'm not in love with you. What this means is:
I've fallen in love with someone else and that must mean that I'm not in love with you any longer and so we must part.
H says: I've been feeling this way for a long time actually and I've been in turmoil. I don't know what I want to do.
H means: I've only been feeling this way since getting involved with someone else. I want to be with them, but I don't want to look the bad guy, so I'll deny an affair when confronted. After we've split up for a while and the dust settles, I'll claim I met OW soon afterwards.
H says: I thought I'd tell you now so that the DCs can have the summer holidays to get used to the idea.
H means: I've booked a holiday with the OW/am getting a lot of grief about going on the family holiday and so I must act now.
H says: There's no point going to Relate, I won't change my mind.
H means: A trained counsellor will see right through this crock of shite because they've heard it all before, so I'm not going to let that happen.
OP, I wrote a very long post last night to a woman in very similar circumstances. Like you, she has had a denial and is in denial herself.
All I will add, because it is relevant to your length of marriage and him not having the common decency to move out and give you space is this:
It will matter to you in the long run if there is an OW, for all sorts of reasons.
Men having midlife affairs after a long marriage tend not to do so because of low satisfaction levels in the marriage. Their reasons for having affairs tend to be a complex mix of yearning for a risky adventure, feeling old and out of potential and being especially vulnerable to someone else giving them adoration, respect and desire. They very often get addicted to the feelings this engenders - and not the person giving it.
It will help your esteem and recovery once you find out the truth, because if he's having an affair, this is not about you and there was nothing you could have done to prevent it. You haven't suddenly become unloveable and it is nothing you've done or said. It is all about him.
If there is an OW in the background pulling the strings, her family situation might have a bearing on your finances. If he intends to set up home with her and help support any children she might have, he will become difficult over money.
You need to insist that he leaves and gives you space, but before he does, get digging for the truth - not from him, but via independent means. Do not believe what he is saying to you - test it out yourself.
I can imagine how awful you're feeling and I am so sorry. It's truly shit. But you need to act tough now, even if you don't feel it. Once he has had a taste of living on his own, or once the fantasy of the affair bubble is burst, he might wake up out of this indulgent middle-aged reverie. If and when he does, you hold all the cards. You might have moved on by then and realised there are actually unforeseen benefits to living without him.
If you still want to fight for your marriage, the only way you'll win is to take control and effect the appearance of starting a new life without him.
Don't beg, don't plead. Get your evidence and send him packing. Keep going to Relate on your own. Keep posting too. You'll get loads of brilliant advice and support.