If you want to divorce on the grounds of adultery, you need to be able to prove on the balance of probabilities that your spouse has had consensual sexual intercourse with a person of the opposite sex.
It is difficult to prove that your spouse has had sex with another without him/her admitting this formally to the Court by way of completing a form. As the Court fee is £340.00 to issue divorce proceedings, unless you are sure that your spouse will admit to the adultery, many would not risk wasting the Court fee and consider issuing proceedings on the grounds of behaviour, which they find unreasonable, and refer to the affair which they believe has taken place as an example of behaviour.
There are some presumptions which may help you, if your spouse will not admit to the adultery, and you are certain that you want to issue divorce proceedings on that ground. The most common are pregnancy outside the marriage eg. your spouse is a man and another woman gives birth to his child during your marriage, or if your spouse and new partner of the opposite sex are living together. Presumptions are "rebuttable" though, and your spouse may choose for example to submit evidence to the Court that there are reasons why he/she is living with another person and still deny that adultery has taken place.
Adultery is therefore not a straightforward route unless you are sure that your spouse will admit to that adultery. If your spouse denies adultery, you may not be able to rely on any presumption and evidence such as phone bills showing that your spouse has telephoned another woman repeatedly, or visited chat rooms on the internet and sent emails, or even been seen together in a pub with another woman, are not sufficient evidence to prove on the balance of probabilities that he has had consensual sexual intercourse with her. If your spouse denies adultery, then you may have to amend the petition to be on the ground of behaviour, which you find unreasonable, which will necessitate payment of an additional Court fee of £200.00.
If your spouse will admit to adultery, it is in fact often a less acrimonious ground for divorce than behaviour which you find unreasonable. You can state simply that your spouse has had an affair with a person unnamed and that you find it intolerable to live with him/her. If you rely on behaviour, you need to give several examples of behaviour which you find unreasonable, which may in fact be more unpalatable to your spouse. You do not other than in very exceptional circumstances, get a larger financial settlement if you divorce on the ground of behaviour, as opposed to adultery. Many spouses, when they come to realise this, will admit that they have committed adultery.