Its not clear from your post if you wish to create the wifi hotspot at the same location as one of the existing mini connectors or at a different location. If at the same location, a wireless access point (WAP) which connects to the Ethernet port of the Mini connector will do the job. Something like the TP-LINK TL-WA801ND 300 Mbps Wireless N Access Point. If the latter, you might want to consider changing your mini connectors to something like these https://www.shop.bt.com/products/bt-mini-wi-fi-home-hotspot-600-multi-kit-084289-BVFH.html
Welcome to this user forum.
As @licquorice has said, the easiest way would be to plug in a a wireless access point into the spare Ethernet port on the mini connector that is by the YouView box end. That is assuming you want extra wireless coverage in that part of the house.
The mini connectors are the only ones approved by BT, for connecting up to the Youview box, so you may have problems if you use any other type.
The the TP-LINK TL-WA701ND or the TP-Link TL-WA801ND wireless access points work just fine.
I have the setup information for the WA701ND, on my website. The WA801ND is very similar.
It meant to say "other end of the house".
Then to ensure compatibility with what you already have, you need to buy an additional single mini connector, and add it to your existing network by plugging it in at the other side of the house. Then plug a wireless access point into the mini connector.
This page tells you how to add another mini connector to the network.