It's slightly annoying to learn that you didn't need the SCART-to-HDMI convertor. But not as annoying as finding out that almost all of these convertors give just the same quality as a SCART-to-RCA-phono lead.
That's right. The vast majority of the SCART-to-HDMI convertors use the video signal that you get from the yellow composite video connection - it's the lowest common denominator - and then convert that to a digital signal suitable for connection via a HDMI socket, but the actual picture quality itself isn't any better than connecting a SCART-to-RCA-phono cable direct to the TV from either your VHS machine or the Thompson DVR.
How I would go about it is like this...
1) If you still have the old TV, or another TV in the house with a SCART socket, then first use that to check the picture settings on the Thompson DVR. Potentially, SCART can work three different ways for picture, but most often it's a more straightforward choice between RGB or PAL/Video. Make sure the Thompson is set to PAL/Video. This goes for using the HDMI convertor too. They rarely work with RGB as a source from a device.
2) Next, the Thomson box has two SCART sockets. One is labelled something like TV, and the second is labelled VCR. Your Sharp TV doesn't have a SCART socket, but is does have a direct video connection> It's the green coloured round RCA socket labelled 'VIDEO/Y'. Buy or use a SCART to composite + stereo audio cable. A cable that is switchable for signal direction is safest.
Connect the SCART end to the SCART socket labelled TV on the Thompson. COnnect the yellow plug end from the SCART lead to the green coloured RCA socket labelled Video/Y on the TV. This will give the picture portion of the signal. Now connect the red and the white audio plugs from the SCART lead to the L and the R sockets to the left of where you've just plugged in the yellow cable plug. You will now have sound.
Switch on the TV and the DVR. Press the menu key on the DVR handset so that it should be showing some sort of onscreen graphic which will make it easier to tell the the correct device signal is being received by the TV. Pick up the TV handset and locate the button labelled "SOURCE" (upper RH quarter of the remote). Press that button and follow any onscreen graphic info about selecting sources. You're looking for something along the lines of AV or Video. When you find this input, you make have a menu choice between Component and Video/PAL. The correct choice is Video/PAL. Make that selection.
Where there's still no pitcture displayed, go to the SCART socket direction switch and toggle the switch to the other switch setting. This should give you the picture from the DVR with its menu overlaid.
3) Now make your aerial cable connections.
There's little point feeding an aerial cable through the VCR In/Out sockets in its own right as VCRs don't have digital tuners. However, you can still loop through for convenience, and also if you wish to use the aerial cable for direct playback from the VCR on one of the analogue stations on the TV.
Loop through from the wall socket and go through the DVR and the VCR aerial In/Out sockets before bringing the signal up to the TV's aerial input.
The RF cable signals from the DVR and the VHS machine will appear only when the TV tuner is set to receive analogue stations. The exact method does vary between brands. Some TVs simply require pressing the TV button to toggle between the digital and the analogue tuners. Other TVs have it listed as a separate menu item.
Once the TV is in analogue reception mode, and either the VCR or the DVR is switched on, you can do an analogue tuning. I'm suggesting this way rather than doing a full auto digital and analogue tuning because you have more control and a better idea of which device will end up on what channel. I would suggest putting the DVR on analogue TV channel #2 and the VCR on analogue channel #1.
After tuning and checking that there's no interference between either of the two analogue source, and that the RF tuning doesn't clash with the underlying digital channels* that occupy the same frequency space, then you can move on to making a connection between the VCR and the DVR.
[* ask me about this if you want to understand more, but the basic plan is to make sure that the RF output channels of both the VCR and DVR don't sit at or close to the digital channels used by the local broadcaster. For example, if your TV is tuned to digital broadcasts on say RF channels 21, 24, 29, 31, 32, 34, 35, 37 and 55, then avoid any analogue tuning at + or - 1 channel space either side of these figures. In the example above which is my local tuning, pretty much everything is out from 21 to 38. I would also avoid RF channels +/- one step either way of ch 55, so 54 to 56 are out for me as well.
Where I live I also pick up some weaker signals from a Yorkshire TV. Even though I'm not using them for Freeview, they're still strong enough to cast noise on the analogue tuning of my Sky box, so I avoid channels 43 to 50 as well.
Tuning improves for me at ch58 up to ch61 where I hit 4G interference. This clears for me above ch 65.
What we have then is 47 possible channel spaces for analogue tuning, but because they share space with Freeview and 4G, in reality I can use just 8 channel spaces for analogue tuning even though analogue broadcasts have long since finished.]
4) Connecting the VCR to the DVR: This is done with a SCART-to-SCART lead. The connection on the VCR is (I guess) the TV SCART unless your VCR has a different way of doing it. On the Thompson box it will be the SCART socket labelled for the VCR.
What this should do for you is automatically route the VCR signal through the DVR when you press play or hit a button that brings up any VCR menu options.
If there's anything such as sockets that are radically different on the DVR and VCR than what I have described then please shout up. I've taken best guess based on the little bit of info you've supplied. However, it is only best guess, so if you can fill in some gaps where something specific is needed then it will help us to help you.
As always, if this or any other answer helped, please click the THANKS button on those posts. It costs you nowt to do and is quicker than typing a post with the words "thanks" 
