A fucker certainly, but I dont think this one's necessarily silly Clara.
The majority of divorces in the UK these days are on the grounds of 'irreconcible differences'; no blame, no shame, end of.
BUT there remains provision within divorce law for an aggrieved spouse to cite any party complicit in an adulterous affair as a co-respondent AND it is within the power of the Court to order that any party so named be liable for a proportion of the legal costs of the divorce.
The unknown quantity here, so to speak, is the OW's dh and he may be less compliant and less easy to bamboozle than the OP.
I reckon that the OP's dh and his OW have planned it so that she'll leave her marital home, or order her stbx out of it, and after a decent interval she'll announce to her family/friends that she has newly taken up with the OP's stbx who, much like herself, having tried everything he could to stay in his marriage (wipes his noble brow) has reluctantly concluded that divorce was the only option.
This could run for a while as, in the interests of financial or other expediency, she may prefer to forestall her stbxh from doing anything rash wait until the ink's dry on her decree absolute before setting up home with the OP's dh.
Meantime, the OP's dh will ostensibly be doing his best short of resuming marital relations with his wife to make his marriage work and no doubt he'll be rewarded by his dps and other relatives praising his stalwart effort when he reveals that he's exerted himself to no avail.
Of course the devil's always in the detail and, if my supposition is accurate, the OP has cause and opportunity to throw a huge spanner into his works by kicking him out now in the hope he may discover that the grass is not greener if he has to live in less comfortable circumstances while continuing his hole in the corner affair with the OW.
It amuses me to toy with the idea of him and the OW arguing over the amount of times she can't see him, the need for them not to be seen together in public, and the lonely hours he'll spend with only the box for company. Or maybe it's pure altruism that's inclining me to the view that their 'lurve' should be tested to the limit before they begin cohabiting?
Alternatively, the OP may prefer to keep the blinkers on believe that the man she married would never stoop so low even though, as he's unashamedly admitted to infidelity, she has little cause to have any confidence that he can't get any lower than he already is