It is unlikely you will get one on the NHS. People treated in fertility clinics will usually get an early scan, but other than that, you will probably have to wait for 12 weeks.
If you are having consultant treatment you can always ask. My consultant sent me for a scan at 6+4 because I needed to be on drugs and they wanted to check there was a baby in there before they started me on them.
Otherwise there are lots of places around the uk where you can get private early scans. These are becoming very popular. Don't get one at 6 weeks though. I strongly recommend that unless you have a need for a scan before, to wait until 8-9 weeks. You will definitely see the heartbeat then and the scan will reassure you that all is going well. There are women on here every day who have had scans at 6 weeks, not seen the baby yet, and spent the next week or two in a panic when in fact nothing was wrong at all.
Usually the NHS only gives early scans to people with bleeding, suspected ectopic pregnancy, or a history of recurrent miscarriages.