There is that to consider, of course, but if you already had an offset, with some existing savings offset against it, then any extra savings will improve your cashflow. Your mortgage could be too small to accommodate the extra savings if they would cause the debt to become negative.
But I take your point. You're saying your mortgage debt is so large that you chose not to place it at the higher rate associated with offsets. Nevertheless it may be possible to go for a "normal-price" mortgage which, although it does not describe itself as "offset" nevertheless permits occasional overpayments and reborrowing.
That doesn't follow, bearing in mind you don't need one which is marketed as "offset" in order to have one which has some offset features. I took out a BTL mortgage branded as "flexible" with L&G (now taken over by NR) which allows you to make reversible overpayments. It calls this building a "flexible reserve" against which you can draw, so you can choose either to take the money out again or take an interest payment holiday, provided the "reserve" doesn't go negative, i.e. the total borrowing would not exceed the scheduled loan balance profile (which in the case of interest-only is equal to the amount originally borrowed, but in the case of repayment is a bit more complicated to calculate, being the amount of debt you would have had at the relevant moment if you had not made any overpayments).
When I sold another property, I put most of the spare proceeds from the sale into this "flexible reserve", leaving only a token net debt costing me a mere £7 a month in interest, and the rest into "normal" savings accounts. The advantage of not having paid off the mortgage completely is that I retain the ability to re-borrow up to 65k for any purpose, whenever I like, without needing to go through a new loan application procedure. So if the right yacht came along, I could augment the fleet and have my tenants pay for the loan.
Meanwhile these "savings" are "earning" me interest at the loan rate of 6% (in terms of mortgage interest I no longer have to pay from rental income). Since this is a BTL, this interest isn't earned tax-free, as it would be with a residential mortgage, since it means my taxable rental profit is now higher than were I to set more mortgage interest against rental income. Alas this "earned" interest is in effect taxed at 22% instead of the 20% normally charged on savings interest. The up-side is that I can have access to an any-purpose loan costing me only some
4.7%, in theory. In practice, since most of my income is below the tax threshold, it will be a bit nearer the full 6%.