Electrical – replace Slater boxless receptacles with conventional ones

You will need to replace them (or get an electrician to replace them).

Replacing sockets is a straightforward job:

1. Turn off the power to the receptacle.
2. Verify that power is off at the receptacle.
3. Unscrew the old socket from the box.
4. Make a note of which wires go where.
5. Remove the wires from the old socket.
6. Wire up the new socket - double checking that live -> live, neutral -> neutral and earth -> earth.
7. Screw the new socket onto the box.
8. Turn the power back on.

This is still a job a householder can do in the UK. However, if you are uncertain about any of the above steps or you think there might be something more serious wrong with the electrics then get an electrician in.

If the plugs aren't holding in the sockets then the sockets are potentially dangerous.

This configuration is a bit odd. The reason why a GFCI outlet has a line and load side is that a single GFCI outlet can offer GFCI protection to any downstream outlets (load).

If I were in your situation, I would install a new GFCI outlet in the first location, and then new standard outlets (your region might require tamper-resistant outlets) in all the downstream locations. This should make troubleshooting simpler, plus you only have 1 GFCI to deal with.

Alternatively, if you do wish to install a GFCI in each location, they should not be wired to the previous outlets load side, rather they should be wired in parallel like standard outlets (either a pig-tail or using the second screw on the same side of the outlet).

If after correcting the installation it is still tripping, then you have a current leak somewhere. A GFCI compares the current on hot and the current on neutral, and if the two are different by a certain threshold, the breaker trips. It could be a device plugged in somewhere else on the circuit, a nicked wire, etc. Start by unplugging everything on the breaker. Plug something into the GFCI outlet - it shouldn't trip, if it does, it's a wiring problem or the outlet itself is bad (if you just replaced it, this shouldn't be the case). One-by-one, start plugging in other devices upstream and downstream of the outlet. When/if it trips, you have found your problematic device or outlet.