close to mortgage neutral

I expect at the end of January to have enough money in various savings and car value to leave around 7k left on my mortgage (if all savings used to pay this off).
The exact amount owing at the moment is about 99k, and I have 15k car equity (which I intend to sell soon and get a new car on PCP) and use the money towards mortgage. 
I have around 77k in various banks and accounts that I will be channeling into the mortgage over the next several months, as and when the fixed terms come to an end. 
I will need to keep some of this money available as an emergency fund so I suspect I will still need a 15 to 20k mortgage when this is done. However, I will be due to remortgage as well and I understand that its difficult to get a mortgage for less than 25k - Is this true ? Should I keep the mortgage above 25k for a while in order to get a good remortgage deal ?
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