OK, so 40 yards is a sizable distance when it involves WiFi signal strength but it isn't out of the ordinary either. If it's in any way practical, using an Ethernet cable is more optimal, so even if it would involve a lot more effort and resources to implement it would be long term benefit. But if WiFi connectivity is your only option, just approach this project from a measured approach, don't just rely upon guesses and supposition. A really vital aspect to always keep in mind is when you're connecting two different routers to each other, both of them need to be configured to work in conjunction with each other (i.e. either two local networks with one router maintaining one and the other router maintaining the other, or one local network with one router being the primary and the other the secondary). You apparently want the latter so be sure to set up one router as the primary, and sole gateway (presumably the Vodafone modem/router), feeding a signal to the other router as the secondary (presumably the TP-Link router) That's also going to involve a carefully set up consideration of just where you position both the modem/router and the router. The configuration aspect relates to how seamless your local network works, the positioning of your routers relate to how well your garden center gets online access.
-- Try following the directions on configuring two routers to work with each other, adapting it to your situation of course (pay attention to the 'bridging' section)
https://www.wikihow.com/Connect-Two-Routers
-- A real deal-breaker when it involves WiFi-to-WiFi connectivity is distance. If the source WiFi signal from the primary router is just too weak, the incoming feed signal to the secondary router is a problem and the emitted signal from the secondary router will just be even weaker. So it's really vital for that secondary router to be well within the effective coverage range of that primary router. And that's where you should ignore the guesswork and instead use actual data to make an informed determination.
First you want to put your primary modem/router in an optimal location so hopefully there's some flexibility on moving it around if necessary. This guide on router placement is worth reading through:
https://arstechnica.com/gadgets/202...ntific-guide-to-wi-fi-access-point-placement/
This requires you to take some measurements and get a good overall sense of where your home has weak and strong WiFi coverage. Install this 'WiFi Analyzer (open source)' app on a phone/tablet.
https://forums.androidcentral.com/e...em.wifianalyzer&hl=en_US&gl=US&token=g_T4xMnh
Use it take signal strength measurements so you'll make a basic WiFi heat map of your home. Use it standing nearby your Vodafone modem/router, then in various rooms, and especially in the vicinity of your garden office. Be sure to check both 2.4GHz and 5GHz bands and pick the best option for the task -- generally 2.4GHz signals can penetrate basic household walls better while 5GHz can supply faster bandwidth, but a stronger 2.4GHz signal is better than a crappy 5GHz signal). The issue here is distance is limiting factor with WiFi-to-WiFi connections and it can have a big effect on bandwidth speed and on latency so you really need to pay attention to making sure that secondary router is getting strong signal to connect up with.
You might find this article interesting, it's a summary of how the author set up their remote WiFi access. Note their scenario involved two buildings that were over twice the distance of your situation so that involved more direct, directional routers.
https://arstechnica.com/gadgets/202...ing-between-buildings-the-cheap-and-easy-way/