Hello and thanks for your question.
I can see how irritating it must be for you to receive a divorce petition based on your adultery when your wife had affairs while you were still together - but unfortunately, until the decree absolute is granted by the court, you are still married and therefore, your new relationship technically does still count as adultery. However, an adultery petition can be very brief and does not have to name the co-respondent (it is considered good practice not to name the co-respondent). In order for the divorce to be speedy the petitioner relies on the respondent admitting to the adultery on the acknowledgment form that you will receive with the divorce petition - which is why the solicitor has written to you in advance to check that you will admit to the adultery.
I think you are wise not to argue with this, but instead to focus on the financial side.
With regard to resolving financial and property matters associated with the divorce, the fact that the petition is based on your adultery should make NO difference to the outcome, therefore you lose nothing by admitting to the adultery.
Once a divorce petition has been filed at court, either party can make a financial and/or property claim against the other - but as going to court is stressful, time-consuming and expensive, if you can reach a settlement, that is to be preferred. Any negotiation needs to be on the same lines that a court would decide the issues. THis means that you must both provide full details of your financial circumstances to each other. The court starts from the position that the matrimonial assets should be divided 50:50 - then looks at reasons why that should not be the case eg if one party has significantly lower income than the other and/or is providing a home for dependent children, then that party can argue for more than 50% eg 60%, 65% or 70% - but rarely more than 70%. The matrimonial assets are everything in your name, everything in her name and everything you own jointly. Pension entitlements count as matrimonial assets.
Without knowing full details of what the house is worth less mortgage, plus any other assets that you each have, liabilities, each of your incomes from all sources, I can't say what percentage of the house you would be entitled to have.
Gathering all the financial information is the first step. Don't rush to make an offer until all of that has been obtained. You can negotiate between yourselves or via solicitors' correspondence or via mediation. The family court anyway now requires the parties to have considered mediation before it will consider an application to court. Here's where to find a local family mediation service:
If you do reach agreement, your agreement can be turned into a legally-binding agreement by a solicitor drawing it up into draft consent order for you both to sign, which is then filed at court for the court's apoprioval. Once approved by the court and entered on to the court record, this is as binding as an order made following contested proceeedings.
You would benefit from some facee-to--face legal advice. Here's where to find a specialist famil law solicitor:
I hope this helps and I wish you the best of luck.
Thanks and best wishes...