Separation and stamp duty?

I thought it was based on purely if you owned a property eg. on the title deeds regardless of marital status or partners.

“does this mean no evidence of separation is needed in which case it could be open to abuse and one of them can end up owning two properties and not having to pay the extra 3%.” Your question is rather hypothetical. HMRC might investigate the circumstances so if the separation is not by way of a formal agreement or in circumstances where the separation is likely to become permanent it could be challenged.

Without an order I think they will be treated as still married

Interested to know your source for that?

Married couples and civil partners are treated as living together (and therefore remain as one unit for the purpose of the higher rates of SDLT) unless they are formally separated under a court order or by a formal deed of separation executed as a deed. The marriage or civil partnership must have truly broken down and it is not sufficient for the couple to be simply living in different properties.
From expert familysolictors.co.uk –
For many couples, particularly those who decide to wait for two years before they file for divorce, they will not have attended to the legalities of their separation before one or other wants to purchase another home. They will continue to be treated as one unit despite having separated and any further purchase will attract the higher rates of SDLT.

I found Patrick Cannon and Cripps saying they would not be treated as still married, I think I would be very dubious about that (as you say in your post). I would love to know their source

From HMRC
If joint owners are unmarried and not in a civil partnership when they transfer an interest in land or property from one joint owner to another then you may have to pay SDLT.
So likely also on new purchases for the unofficially separated