A lot depends on your interest relief situation. If you have a big mortgage and are paying plenty of interest, the S23 relief on your income won't be much good to you because you already have the interest to set against tax (called the 'tax shield' in the jargon). Unless you have a lot of properties, it won't be worth your while having the S23.
If, on the other hand, your mortgage is nearly paid off, even on a single property, it may be worth having the mortgage interest relief. This may make it possible to buy and rent the new property without having to put up any more cash than you are putting up at the moment to pay the tax.
The tax relief does have value, and you can sell it with the property if you can't use it all. It potentially has the value of the amount you can save in tax (i.e., top rate of tax x percetage relief on property x value of property), in practice it is going to be a bit less than this, maybe 10 or 20 percent less.
But you can't untie the tax relief from the type of property. Section 23 property is by its nature non-prime to some degree, so you have to be taking into account how you think that particular area is going to appreciate.
If you have another property nearly or mostly paid for, then the fact that you can only get a lower LTV on the new property is basically moot. You can borrow against the existing property.
You just have to work out the cashflows and decide if it is worth doing for you. If you don't know how to do this, find an adviser who does. (Although in my experience, this is hard to do.)