New ISP, new router connect to old one. Help!

I've just switched ISP (from Virgin to EE) and need a little advice...

My old (virgin) setup was as follows:

1. Virgin router, in modem only mode.

2. The virgin router (modem) has a wired connection to my own wifi router (a TP-Link N600 I think).

3. My TP-Link wifi router has a wired connection to my NAS (a Synology).

New setup (EE) consists of a EE BrightBox router, so far.

I've tried getting the NAS working wired in to the EE router. No joy. In any case, even if I did, that may not be a great setup for me, as the router won't be as configurable as my own TP-Link router. Also, prefer to not have the NAS downstairs next to the EE router.

Is it possible to connect wirelessly from the EE router to my TP-Link router? I had a look at WDS (http://www.tp-link.com/us/faq-227.html) but, no joy.

Also, wondering if I can get another device that will connect wirelessly to the EE router, and plug in (network cable) to the back of my TP-Link router where the old cable from the Virgin Media modem went in to provide internet connectivity. Something like one of these:

https://www.amazon.co.uk/s?url=search-alias=aps&field-keywords=wireless+wifi+bridge

Will that work?

Any other suggestions?

Thanks.

As far as I know all EE routers have locked settings which cant be altered. It stops them being used for other things or other ISP's, so that may be the problem.

Update.

I've managed to get the NAS working while connected via network cable to the EE wifi router.

Not entirely ideal, as I'd like the NAS upstairs away from the router.

Also, I'm wondering how network speed will compare; will EE router be as fast at sending files internally on my home network, as old (TP-Link N600) router was?

---------- Post added 10-11-2017 at 14:45 ----------

Looks like EE router is doing 100mbs wifi speed. Sure my old one was 1000mbs. Testing file transfer speeds...

---------- Post added 10-11-2017 at 15:29 ----------

Yep, old wifi router is allowing much faster (about 2.6x speed) file transfers compared with new one.

So, can I use one of the following, plugged in to the back of my own wifi router (where the network cable coming from the virgin media modem sits) allowing it to access internet from the EE router?

https://www.amazon.co.uk/VAP11N-300-Wireless-Repeater-Partner-Dreambox-White/dp/B01G1I38LW/ref=sr_1_4?ie=UTF8&qid=1510317298&sr=8-4&keywords=wireless+wifi+bridge&dpID=31L9Dbgn7DL&preST=_SY300_QL70_&dpSrc=srch

---------- Post added 10-11-2017 at 15:46 ----------

Okay, just tested it with a network cable from EE router going in to my own router, and that works just fine. Can't see any reason why one of those wifi bridges won't work. Unless I'm missing something?