Clicked a fake Royal Mail link, laptop full of pop-ups now

I clicked on a link in an email that said it was from Royal Mail asking me to pay a small redelivery fee. Since then my laptop has been popping up loads of warnings saying I have viruses and my browser keeps opening new tabs to dodgy-looking websites. I've run a free scan from Avast and it found 47 'threats' but won't actually remove them without me paying. I'm not paying them. Need someone in Birmingham to come and clean it properly, and also tell me if I need to change any passwords. I bank online so I'm a bit worried about that side of it.