TUPE'd with no contract of employment

The company I work for has just been taken over by another company and as far as I can gather we have been TUPE’d, is this correct? I have no idea of this, as this is the first time this has happened in 27 years.
I hadn’t been given a written employment contract before we were taken over, which to be honest that doesn’t really bother me, as all I am interested in is the hourly rate and guaranteed hours, holiday entitlement is the standard 28 days.
From what I can work out myself is, they can’t lower your hourly rate even though there own drivers are on less, they have to honour any holiday pay you haven’t taken before they took over.
Main question is, am I still able to refuse to sign a contract of employment with the new company.

Depends if you want to work for them or not I’m guessing ?

I will rephrase it, can they ask me to sign a contract which would change my terms and conditions?