We are hoping to buy a house also for around 200-250k. Less if we are lucky and things go our way in the coming months.
Unlike yourselves, we don't own any other property.
However, with interest rate rises etc. a 100k mortgage over 25yrs, repayments (incl. insurance) near enough equal the 600pm rent we are paying now. Banks will only offer a mortgage of about 100-140k max mortgage on one salary of 40k if you have kids (from my experience, that was a year ago we last checked).
So its a balancing act for us to keep a biggish chunk of savings as a safety net.
For example if one of our cars packs it in and all the savings gone on the house, we'd then have to borrow a car loan and that would impact the cash flow.
If you spend your whole lump sum, and still have a mortgage equating to your current rent, you won't have the interest on savings for the extra big spends.
So sometimes it might be better for the next few years to try and keep mortgage repayments small by other ways (like taking the longest term possible depending on your age), to keep a chunk of savings. So that in your eagerness to be prudent and reduce debt, that you don't end up living a penny-pinching existence. Leave as many options and as much flexibility in it as you can.
I'd be slightly worried about the investment property - the value of house and the mortgage owed are only about 35k in the difference.
Have you applied for another mortgage recently or spoken to your bank's mortgage advisor, do you know how much they would allow you to have considering you have another house as well?
Banks don't take much heed of how much savings you have because, like, you could put it all on a horse tomorrow. They just look at salary, how much you want, ability to repay, and long-term debt that could impact ability to repay.