Hi tk96,
Your marriage contract would not count towards a Capital Gains Tax liability in the UK.
As you are the beneficial owner of your share of the asset, you would be chargeable to cCpital Gains Tax on your share.
As there is no charge to tax on the transfer of assets between spouses, you could consider gifting part of your share to your spouse, before the sale of the property.
This would be a legal matter, which we cannot advise on.
Capital Gains Tax: what you pay it on, rates and allowances
Thank you.