Injured at work then furloughed

Overtime constituted 50% of income Now receiving 80% of basic. Please advise. Thank you.

Provided your overtime payments are not discretionary, then they should be counted in calculation of the 80% of "wages". If they are not, nod your payroll person in the direction of this https://www.gov.uk/guidance/work-out-80-of-your-employees-wages-to-claim-through-the-coronavirus-job-retention-scheme#include

But as above, unless you have a really shiny sickness policy, you're going to be earning more on furlough than sick so don't get taken off furlough to be put on £95 / week sick pay

Do they have a right to put you in furlough in your contract?

If not then you have to agree to go on furlough. 

You and your employer can agree any amount as between yourselves for how much you get paid.  The question is then what can the company claim back from the government - the overtime aspects of which are "complicated" as set out in Escaped's link.