Of course, not everybody would exploit it for nefarious ends but just keep in mind the sort of people that would do have an excellent knowledge of networking, are determined and are quite happy to reconfigure something even if it doesn’t work out of the box.
On the bright-side you’re right about the Wi-Fi. To get a signal stable enough to work on they would probably need to be within 50m or so. On the not so bright-side, if they have your router password and it allows remote access they could make use of it even if they were on the other side of the world.
As you are now an EE customer, you need to post on the EE forum https://community.ee.co.uk/, you may be able to get more help there.
EE are a separate company within the BT Group.
@Teza I suspect you are worrying unnecessarily, can't imagine many tradesmen will be rifling through your files.
The simplest solution is to just change your WiFi password temporarily and give that to tradesman. If you have to use your laptop/PC whilst he is there, just turn off network discovery to prevent access to your files.