If you increase borrowing on a buy-to-let property and use this money to reduce the mortgage paid on your residential home, where tax relief is not granted, more mortgage interest is paid on your rental properties, where tax relief is available. However, you must bear in mind that tax relief is only available on borrowings up to the value of your buy-to-let property at the point at which it was first let.
Clearly restructuring your borrowings in this way would need to be done correctly in order to make the tax man happy - so you would need to employ the services of a qualified accountant. In all likelihood you will need to set up a buy-to-let business account and pay all rent into it and pay expenses out of it. Ultimately any profit on your buy-to-let business could be used to reduce the mortgage on your own home.
The net result - tax efficient borrowing.