You can have as cheap a time in Europe as the UK if you're prepared to plan carefully. You may need to stay in cheap chain hotels, though booking early will generally get the best deals from nicer places - and booking direct, rather than through a third-party website like Booking.com, will normally get the best price of all (especially if you're prepared to phone up and ask if they do a biker's discount - some places will, though not the chain hotels, and never by email - only on the blower).
As I claim for lunch when I'm working (which last year included more than 20 days in France) I can assure you that lunch on the road over there always costs the same as lunch on the road in the UK; there's a pound either way in it and often my French cheapy lunches are a bit more expensive – mostly because soft drinks are notably and oddly pricey in France. To keep costs down your best bet is to stock up with lunch-type stuff at supermarkets or bakers (remembering that in France the shops shut at lunchtime: get your supplies at 11am). Evening meals are usually more reasonable than eating out in the UK, but it is still quite easy to wander into a posh restaurant that's more expensive than eating in a nice British pub - check the menus before going in. Petrol will be a similar price, but you're likely to do more miles so - overall - you'll spend more on fuel (and if you need to use motorways to cover distance in a hurry, you may also have tolls to pay). Plus you'll have to pay for your crossing to get there.
On top of which, of course, the exchange rate means your money won't go so far as it used to. This thread made me go back to my expenses and do a few sums: if I was to redo any of my pre-Brexit-vote trips at today's exchange rate, they'd be 15-20% more expensive. Which makes me realise that this year I'll have to go back to camping, rather than staying in hotels, when I go to France on my not-work trip to the Alps.
My rough league table of most-expensive-countries-to-visit runs: Switzerland, Germany, Austria, Italy, Posh France, Holland, Belgium, the rest of France, Spain, Portugal. I split France between the posh bits (the Riviera, cities, tourist traps, etc) and the rest, because there can be a massive difference in prices between the charming, catering-for-locals villages of the Auvergne or the Limousin and the prices you'll pay for anything in Biarritz or Cannes or a Loire chateau. And even the affordable bits of France are way more expensive than Spain.
But. It is still definitely worth going to Europe. Absolutely. It's amazing. It'll feel much more like an adventure, somewhere fresh and fun and exciting.
Just plan carefully, book wisely, avoid the quaint tourist cafes where it's 1 euro for a croissant and 2.7 euro for a coke... and just enjoy yourself. It'll be amazing.
ETA: The actual question was: will there be a decent saving? Answer: probably not. You can probably do a decent UK tour for £10-£15 per head per day less, which does add up over the course of a week to being £150 or more for the two of you. But the holiday you can have in Europe is going to be way more than £150 better!
