im not expert but here is my opinion, u both are doing really well on saving. you reached 10% why not go a bit more, it will def help you in the long run! also as the current market slump i dont think u be in a favourable state to get a mortgage yet as you dont know if the market will drop a further more % then ur just losing your deposit.
and yes parents can be a nightmare but its not all bad, i reckon you should carry on saving more, the more you have the more better rates you will get! and no rush, markets bad so wait for the right time. just think you said 2 more years and the defaults will go, you can save a further 2 years and by then the economy in uk would hopefully repairing itself again so then you have a
1. no more bad credit under your name,
2. you both can be on the mortgage.
3. you have a much higher deposit therefore the rates will be very good and you will be paying less for your mortgage (every little helps)
my dad is a very ambitious guy and ever since he's always told me think far ahead before you do anything, it may be good now cause its immediate but it may affect you later on and it comes back and bite you.
i hope it helps.