New mortgage with fair credit rating

Hi. I hope someone can give me some straight advice

My husband and I need to move as we need more space for our growing family. We have held our mortgage for over ten years now and never late . We earn over 70k in joint income and have 20% deposit for the new home that we are interested in.

If we manage to sell our current home I am worried we will not get a new mortgage deal as I have a fair credit report. I have late payments on a next account (all 1 status) there are a number but all before 2011. This account is still open but with a zero balance. I also have one late payment ( again status 1) on a credit card from June 2012. This was just a silly error. This card is now clear and closed.

So in summary apart from my stupid late payments in which I am to blame for we have no other worries. My husbands credit report is clear and our only debts are our car finance. We have secure jobs and have been with the same employers for over ten years.

Is a new mortgage possible with 20% deposit and these late mArks? We are only looking for just over twice out joint annual income.

Thank you for reading and thank you in advance for any help. Worrying myself sick...