Should we stick with our current provider or try to remortgage despite husband's poor credit.

RMLHV

We are currently with TSB with a ported mortgage, £194,000 total (house value £300,000). £50,000 on a 5 year fix until November 2025 and £144,000 on a 2 year fix until July 2025. 
Since we moved we have had to stick with TSB for remortgaging as the smaller portion was still on a fix so I was hoping next year we could look at applying for other deals with other providers and combine the two parts. 
However, it has come to our attention after my husband applied for a loan and was rejected that he has a poor credit rating due to a missed payment on his phone bill 3 years ago. We have always just taken TSBs best offer and not had to actually apply for our previous remortgages (2 in that time) so it wasn't something we were aware of. 
My credit is very good and I am the higher earner; I earn £52,000, my husband is self employed and earns roughly £25,000. 

Is it worth trying to apply to remortgage next year and bring the two parts together or will husband's credit score be too much of a hindrance and are we better off just sticking with whatever TSB offer for both parts separately for another 5 years and try again after that term and hopefully this black mark against my husband's credit has been removed? 

Thanks 

Brie

Have you had a look at his credit reports to see if that's the only issue?  Is he registered to vote?  Sometimes it's only when someone looks at the reports does something pop out.  Most common is a PCN that has been missed and has become a CCJ.  Or sporadic late payments on credit cards which raises the risk on a person.  

If it's just the phone bill 3 years back that should fall off the report in another 3 years. You might take a shorter term remortgage (2 years) and hope that the phone issue is enough into the pass to no longer be an issue.