It can be tempting to name the person with whom your husband/wife has had, or is having, an affair, but it is almost certainly not advisable to do so.
The current format of the divorce petition is based on a law that dates back to the 1970s. At that time, if you wanted to pursue a divorce petition based on adultery, then it would be highly likely to mean a court hearing before a judge, with evidence being given of the adultery or unreasonable behaviour in question. In that situation, you might well want to include the other person in the proceedings and have them attend the hearing to give evidence.
These days, the court discourages hearings in relation to divorce petitions and well over 99.9% of them proceed solely on paper. The divorce is likely to cost you £550 for a court fee (unless you are receiving state benefits), together with any legal fees that you spend, which should not be much if you use us or do it yourself.
Adding a co-respondent by name to your divorce petition is one way to potentially increase your costs exposure, as there is a potential for that person to obtain a costs order against you.
If you add a co-respondent it will not change the basic nature of the divorce that you ultimately obtain, and it will not give you any advantage in any other possible sphere of argument with your former spouse. Much better to save yourself the cost and possible emotional hassle and keep the petition between you and your spouse. If you really must spend money on lawyers, save it for an issue that is worth arguing about and where you can make a difference (arrangements for the children, or division of the finances), rather than something which is ultimately going to make no difference to anything – your decree absolute will look exactly the same (and have the same effect) whether you have named a third party or not.