Lets play this scenario out a bit... you add £10,000 to the mortgage, thus clearing your loan. You keep the mortgage payment the same as it is now, with the aim of paying off the mortgage quicker than the current length of the mortgage.
What happens when you next need some money, where does it come from? Will you use a credit card, take out a loan, remortgage again?
Debt is a symptom, you need to tackle the cause. You need to look deeply at your finances and make a determined plan to remain debt free and to work towards paying off the mortgage over the next 10-15 years... before the children have left home! You can factor in to your plan having time off work to have another child and to factor in the costs of having growing children.
If you are going to move this loan to the mortgage so you can start again by having no debt other than the mortgage, plus you will do a monthly cash flow plan, put money aside for emergencies, put money aside for retirement, put money aside for the ever growing needs of your children, then maybe it is a sensible decision... but only a decision that you and your partner can make.
Alternatively you pay back the loan as fast as possible by getting really determined about repaying debt and then saving for the future, so that by the time child no.2 comes along you don't have the loan any more.