Upvote:1
You are free to leave the Schengen area so there should be no problem leaving Czech Republic. You also should have no problem visiting the UK: the border officer just needs to be satisfied that you can afford your visit, have a genuine visitor purpose such as tourism, and won't overstay. You will be able to show your onward ticket to SG, bank statement or other funds, and some paperwork from your university showing that you need to go to Singapore to complete your course. Nobody on the internet can guarantee you will be able to enter the UK, but it seems to me that your circumstances are those of a genuine visitor.