A DHCP client performs the first and third parts of a four-stage process that is a more complicated, though entirely straightforward, version of what you mean by "say".
The phases are 'Server Discovery', 'IP lease offer', 'IP lease request' and 'IP lease acknowledgement' - the second and fourth stages being performed by the DHCP server. This is commonly known as "DORA": discovery, offer, request, acknowledgement.
The client needs an IP so looks for any available DHCP server, the server receives this discovery request and offers an available IP from its DHCP pool, the client confirms it will take that IP and the the server acknowledges this.
As you commendably seem to be persevering with this (sorry, that sounds patronising and it's not meant to!) having as clear as possible an idea of what is actually going on will help. Moreover, this points out the difference between a DHCP client and a DHCP server in case there is any confusion there.
Which leads us into your last paragraph... no, switches don't work the way a modem/router does, and they don't assign IP addresses. They work at the Data-Link layer, sending data as 'frames' between MAC addresses, whereas routers work at the Network layer *, sending data as 'packets' between IP addresses.
As others have already said, you should manually assign your switch an IP that is outside the DHCP pool on your DHCP server (your PlusNet router), but it can get an IP via DHCP - and indeed probably defaults to that out-of-the-box for easier setup - and in this scenario it is functioning as a DHCP client. It is doing the D and R in 'DORA', not the O and A.
So many consumer devices these days are jack-of-all-trades, at least if you want them to be, so despite what I said above about layers 2 and 3 it is possible that your managed switch has a DHCP server bundled with it and that when you say you are "enabling DHCP" you are turning on an additional DHCP server (to the one on your router) rather than telling the switch to get its IP via DHCP. If so, this would be <Trump>Bad!</Trump>
As your PlusNet router is already functioning as your DHCP server you don't want anything else trying to do the same job. I'm oversimplifying but you can think of them as fighting over the DHCP clients and potentially causing DHCP failures. It could be at least part of your problem, if not the whole thing. Another reason to manually assign the switch's IP - so every 'DHCP' option on your switch can be disabled for minimal confusion.
* N.B. for other techies: yes, this is not the only over-simplification here but I have deliberately left out any mention of Layer 3 switches, subnets, VLANs, superscope etc. to try not to complicate matters any more than necessary
Edited by deleted (Sat 18-Nov-17 16:38:22)