I think £39/month (minimum) is very expensive for this type of app. In order to start seeing benefits over other apps which take 10%+ in commissions, a takeaway would have to see at least £400 in orders per month. Now, an average order is probably around £15-£20 so this is 20 orders/month or 1 order per day.
If they don't reach that, they are clearly losing money. In order to see these level of orders, they'd have actively promote this app among their existing customer base and recruit probably 100-200 users in month 1 to start seeing some orders. This is additional effort which does not really bring much value anyway, neither to the business nor to the customer who "is already calling".
Additionally, this will not help in bringing new business (well, if it does from the QR codes on the front window that's probably a marginal percentage) - something the other apps certainly can do to some extend.
One may argue this would allow streamlining the ordering process but majority of orders (or significant proportion at least) would have to go through this channel - this is extra hassle of monitoring the system and checking whether on order has appeared.
Another point might be that the app might increase purchase frequency. I think people work out what they want first, then order so probably very few cases - definitely niche target group (there was a thread a few month ago around this, loads of comments - worth digging out).
I reckon, it's a proposition for a very small group of customers and large chain takeaways or the ones with large marketing budgets (so big ones). Also, you've already worked out your price points already without (presumably) proving the concept first. If you are keen to go ahead, I'd probably think about trialing it first (no charge but work hard to prove it works with a few trialists) to build a business case which may support future sales. Also, worth considering "freemium" or "entry" levels with limited functionality to get more businesses on board.