I used phones without a cast feature to a non wif enabled tv, and still do. I only cast to a hotel Samsung tv, and now I find the 2nd generation Chromecast better than casting (£17 nib clearance at John Lewis) I don't know about the Leelbox - I presume it needs a power cable too, the hdmi won't power it. If you can get a cheap Chromecast, even gen 1, however I needed a second phone to set up the newer Chromecast, or a cheap mifi device with another sim or your main sim transferred temporarily.
With the newer, but now old Chromecast 2 I recently bought, I can just use 1 phone with my main sim to stream to the tv / Chromecast - however I needed a second phone on wifi off the hotspot to use the Google Home app to set up the cast function initially. Actually I put my sim in the other phone to set it up using my main phone on the WiFi connection so it will be recognised with the sim back in later.
It's a little involved though easy enough. The Home app asks to turn on Bluetooth and wifi to set the Chromecast up.
If you can pick up a Chromecast, and temporarily use another Android phone or get a cheap mifi device which I've also used, you should be good.
Otherwise maybe ask in a CEX store to look at cheap (Samsung) phones that may have a cast function, but I don't think they will work on a non wifi tv.
You don't necessarily need a large hotspot allowance on your sim plan, I think. I used a mifi device when I didn't have much hotspot data, but most plans don't differentiate these days. True of Three and EE at least.
(I think maybe Miracast is now an old name from 2012 and most newer tvs have a cast function with wifi)