Given each constituency does its own counting and all checking is done on paper, I think it's actually very difficult to stop somebody from voting twice in different constituencies. AFAIK, there's no nationwide cross checking to verify that "Lucy" only voted once (and suspect it's way too difficult and costly to do so). How would you expect an investigation to spot that a person has voted twice in separate constituencies? There are a lot of people called "John Smith" in the UK.
On the other hand, I'd be amazed if such behaviour is very widespread.
All that said, I would like to see voting in the UK move into the 21st century.
One quirk is that if you're a student living away from home you can vote either in your home constituency or the constituency you've moved to. You're not supposed to vote in both, but I too struggle to see how it can be spotted that you've voted twice in different constituencies. A recent poll indicated that the vast majority of students voted in their home constituencies, so there's an argument for changing the law so that you can only vote in your home constituency if you're living away at university.
I too would like to see voting modernise and it's why I don't understand some of the opposition to providing ID to vote. You need ID for other things such as collecting a parcel from a Royal Mail Sorting Office and at the moment, all you have to do is say your name and that's it - no need to show ID or the poll card you get posted leading up to it. I don't believe there are widespread cases of voter fraud in the UK, but I don't see that as a reason to have a lax system of verifying ID when you go to a Polling Station.
Well if Corbyn wins and need the LibDems to get the majority, there might be a people's vote in the near UK's future.
Both Labour and the Lib Dems have ruled out entering coalitions and the Tories have told Farage where to go with his offer to form a "leave alliance", plus I suspect the DUP are too hacked off with Boris to sign up to another "confidence-and-supply" deal if the arithmetic meant the Tories needed the DUP to get majority votes in Parliament for things such as the Queen's Speech or the Budget.
It wouldn't surprise me if, in the event of a hung parliament, Labour are more likely to grant the SNP a Section 30 request for a second Scottish independence referendum in return for support over a Queen's Speech, Budget etc. if the arithmetic meant a Labour/SNP majority was possible. However, there's been mixed messages over what Labour would do in the event of a Section 30 request being put in. It would also not surprise me if the Lib Dems back Labour with their pledge to hold a referendum despite the Lib Dems' policy being to scrap Brexit altogether.
All the talk about refusing to form coalitions are just a ploy to boost their support. If the arithmetic produces no clear majority for one particular party, you can bet all parties will be looking at what they need to do to get others on board in an attempt to command a majority and claim a right to govern. The last time we had this sort of scrambling was in 2010.
One poignant quote Nick Clegg came out with in the immediate aftermath of 2010 is that the Tories should have the first shot at attempting to form a government by way of them being the party with the most seats. It wouldn't surprise me if whoever has the most seats but not a majority will parrot the same line in an attempt to claim they have the right to have the first attempt at forming a government.