Going abroad without my childs father

[Loganoshea06]

I am looking at going away for a week next year and was wondering if I need my babys dad's signature on a letter , our baby is in mine and his last name as its double barreled . Does this mean I won't need a written consent just their birth certificate

No, you need written consent, the details are on the gov website.

https://www.gov.uk/permission-take-child-abroad

You may well not be stopped and asked, not every lone adult travelling with a minor is, but you might.