There’s no sensible or financially conducive reason whatsoever for you to jointly own two properties with an ex partner, when you don’t plan to live in them together. He should buy you out of the one he resides in and you buy the second as your only property and pay lower rate stamp duty accordingly. Otherwise you both have to suck up the second property SD, like the rest of us.
But, honestly, if he is your ex, then separation of finances should be a natural joint goal?
Oooh, except is the issue that he cannot afford to fully buy you out/raise a mortgage on the current property, so needs you to remain on the current mortgage? By contrast, he IS able to get an additional joint mortgage on the smaller, cheaper one you are living in?
if so: then you need an alternative strategy. Essentially he gets a mortgage for what every he can raise and and you transfer the property into his name BUT the difference between his mortgage he raises and the outstanding value/amount he needs to give you would be treated as a loan. {eg your half share is £150k, but he can only raise £100k. He gives you that but he would owe you £50k. This would be regarded as a secured loan.] You get a solicitor to draw up a contract that clarifies it is a loan for £x [outstanding] amount, at x% interest, to be repaid in full by x date (or in instalments). Ideally this should be secured against the property, but would not be considered a share in the ownership, just a ‘charge’ against it. Your name comes off the title deeds as a joint owner, but moves down the deeds to register your charge/financial interest instead. A solicitor can advise.
Then you take what he has raised via mortgage and buy the second property/get a mortgage yourself as sole owner in your own name? No increased stamp duty, no blurred lines in terms of finances. No issues at a later date if either of you start cohabiting with other people who might accrue an interest in one of the properties, no issue about evicting those partners should your ex die and you need to claim your share of the other property etc. Financially, a clean break.