You might win big on the premium bonds, but could equally, and actually more likely to, come away with less than you would just putting the money in a savings account - the odds of winning very big are actually very small. The more you have, the more likely your prizes are likley to be in line with the average prize rate of about 1.4% ish.
Depending on the interest rate on your mortgage, I would possibly put £30k in PBs, £30k in the best fixed rate savings account I could find and pay £30k off the mortgage, but only if the rate is higher than the 1.5-2% you could get in a cash savings account. If your mortgage rate is much higher than 2%, perhaps put just about all the money in the mortgage (check for penalties) and then use the money saved by not paying a mortgage to then save in cash and PBs.
Perhaps keep another £5-10k in cash over and above the £10k for home improvements if you don't already have this sort of money available, although you can get money back from the PBs fairly quickly should you need it.
I wouldn't do another buy to let going forward, as you will have to pay more stamp duty, but you have previous experience of being a landlord, so will be better placed to decide whether you want to do this again - potential for profitability obviously depends on local prices, rents, demand etc.