You are basically on the right lines in your thinking on SM.
"I understand Spousal Maintenance seems to be based on need not want?"
SM is based on need, but also on standard of living during the marriage and on level of disparity between the parties earning capacity. So with a very high earning husband a wife who gave up her career to look after kids may well be awarded SM that is beyond basic needs.
"Does the fact she is now living with someone else have any bearing on SM payments I may be judged to pay?"
Yes it does. If the cohabitation is admitted by her and considered by the court to be the start of a permanent arrangement then it could well reduce SM. This is because her needs or outgoings are reduced due to having someone to share the bills. It could possibly even reduce SM to nominal SM (1 pound /year) for a few years as a safety net in case her new relationship breaks down.
"Am I correct in saying if she can support herself I am not obliged to pay SM?"
This is a slightly grey area. The question is whether the recipient of SM should be entitled to enough SM for a basic standard of living, or enough to live in the same style as they were accustomed to during the marriage. The best answer I can give is that the latest caselaw is pointing towards a principal that the SM payment should be at a level, and for a term (length of time), that allows the recipient to gently transition from the lifestyle they had during the marriage, to the one they could expect as a self supporting individual. There should be no long term expectation to be indefinitely supported on same lifestyle as they had during marriage.
"Oh and how can it be proven they are cohabiting if not admitted by my ex wife?"
Try to obtain written evidence of her partner paying bills/financially supporting her. A bill or two in his name, but with her address on, would be ideal.
"Would it have a bearing on the split of the house?"
Not sure what you mean by it (the co-habiting or the SM?)
But both have a bearing on the split of the house.
The court is aiming to re-house both parties using the assets available. If she is co-habiting it increases her ability to get a mortgage and that means you have a greater chance to get 50% of the house.
SM also is related to the capital split in that in situations where SM is payable, the level and term of SM can be reduced or even eliminated by trading away more of the capital. You can achieve a Clean Break
with no SM by capitalising the SM (paying it all in one lump sum out of what was your share of the capital).