What happens if you only have £50 left on your mortagage account??

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So we've recently made some changes to life style, and current on a drive to save and maximise savings.
We have a small mortagage left on our house, but it's a 5 year fixed, with 2 years left to run. We've been over paying, and could clear it tommrrow but over-payment penaulty is quite substantial (£800 worth of interest), so plan is to continue to over pay the next 2 years and than plan to pay off the mortagage....
But in 2 years time, we'll still have 10 years left to run on the mortagage, and given the low interest rate, it may serve us a source of 'cheap' borrowing, about 1.7% I think at the moment.
So if rather than pay the full amount off in 2 years, we left say £1000 in the mortagage, and kept the term/length of the mortagag the same, potentially we could 'Tap' into it in the future by re-mortgaging £20-30K etc...and than pay that off at our lesuire...
Than I thought what if we only had £50 left on the mortgage, with the same 10 year term. Surely works out at something like £1/month for 10 years...Which is a very cheap 'fee' to pay to have access to cheap borrowing....
Have anyone done this? Or is there some kind of clause the contract that will stop me from doing this?
We have a small mortagage left on our house, but it's a 5 year fixed, with 2 years left to run. We've been over paying, and could clear it tommrrow but over-payment penaulty is quite substantial (£800 worth of interest), so plan is to continue to over pay the next 2 years and than plan to pay off the mortagage....
But in 2 years time, we'll still have 10 years left to run on the mortagage, and given the low interest rate, it may serve us a source of 'cheap' borrowing, about 1.7% I think at the moment.
So if rather than pay the full amount off in 2 years, we left say £1000 in the mortagage, and kept the term/length of the mortagag the same, potentially we could 'Tap' into it in the future by re-mortgaging £20-30K etc...and than pay that off at our lesuire...
Than I thought what if we only had £50 left on the mortgage, with the same 10 year term. Surely works out at something like £1/month for 10 years...Which is a very cheap 'fee' to pay to have access to cheap borrowing....
Have anyone done this? Or is there some kind of clause the contract that will stop me from doing this?
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