…thus the old term for ground beef “ground round”. A good choice if you’re planning to grind your own hamburgers, although you’ll have to add some fat to make an acceptable burger. A 0% fat burger is inedible.
Yup, what we have here is a (quite nice-looking) bit of silverside - carefully trimmed of all fat and membrane, then tightly wrapped in plastic film to make it look smoother and more uniform than it really is.
When I unwrapped it, it was conspicuously quite coarsely striated along its length - sliced through, there wasn’t much marbling, but there’s a web-like network of connective tissue amongst the muscle fibres.
As a final test, I cut an inch-thick steak and bashed it with a wooden rolling pin - it was quite resilient - I would have expected fillet to break apart under this treatment.
So I’ve cubed it and frozen two thirds - the remainder I will put in the slow cooker tomorrow to make a filling for a meat pie.
Meanwhile, I may report the store to Trading Standards, as this is a fairly clear case of deliberate mis-labelling - it would have been a bargain for fillet, but it’s expensive for silverside.
If it it were horse, they’d have spelled it filly. 
Not a butcher, but based on my experience peering closely at labels…
There are a couple grocery stores near here that sell “filet of beef” and “filet mignion”, and they are two different cuts. Filet Mignion is beef tenderloin, the expensive steak the OP is thinking of. Filet of Beef (in my stores) is a piece of chuck tender. Filet of Beef is also used for other cuts, as someone else mentioned.
I don’t think you’re in the same country as me, and the terminology is different, as noted upthread.
Can’t resist: recipe for Tournedo Rossini. Take one hunk of of tenderloin, anything but the filet mignon. Saute. Add foie gras. Add truffle. End of Recipe.
Apparently a restaurant or two in NYC has brought this dish back from the good old days.
The filet of beef, in whole or chunked for a stew, is eminently suitable for long cooking at low temperature (“low and slow”). This way the chewy cartilage running through the muscle softens and melts and adds wonderful mouth feel as well as allowing the flavor of the meat to spread around when you eat.
Since all the surface fat has been removed, you may want to slap some fat (unsalted fatback) or simmered-for-a-while–to desalt and lower the smokiness, respectively–salt pork or bacon (“rashers,” for Brit-only speakers) on top of the roast. This is called barding, BTW. It is often confused with larding, which you can do instead, if you feel like running strips of fat with darning needles through the meat. If for a stew, throw in some pig skin, or, since that may be hard to find, a split-up veal knuckle or cow hoof or a split up pig’s foot (trotter).
You may also want to brown the stew meat or whole roast on the stove first, which adds that type of tastiness.
Now I’m hungry for some London broil.
London broil with a vegetable prepared á l’anglaise: briefly boiled and served without a sauce (peas and small onions, say).
Or skip the London broil–or eat with it, if you’re hungry–a veal or chicken cutlet á l’anglaise: the cutlet floured or crumbed, or both (with an egg wash after the flouring so the bread crumbs adhere), sautéed in butter.
A dish curiously unavailable in London and its environs (particularly since Britons don’t use the word broil).
For the record a traditional filet is a steak (appx 2" thick) cut from the tenderloin. A filet mignon is a filet cut in half.
Any chance it was a hanger steak?
It’s one of my favorite cuts, but it tends to be cheap because it isn’t very popular and it can be really tough if you don’t cook it right.
Nowhere near as much marbling as that (that looks nice).
I cooked 1/3 of the beef (which I am certain is silverside/round) today, cubed, fried to brown in bacon grease, then stewed for 8 hours in the slow cooker with onions and stock - it’s come out lovely (although if I’d known I was buying stewing meat, I’d have chosen brisket or flank).
They say “grill,” right?
I never thought of it before, but when Americans say “It’s broiling hot out” to a Brit ear that sounds strange?
Do you really say “broiling” in that case? We say “boiling” and that’s what I’ve thought I’ve heard. Actually, your way makes much more sense!
I’ve heard both broiling and boiling when referring to how hot it is outside. In Houston and other tropical and highly humid areas, saying that it’s boiling hot out isn’t too far off the mark! 
Both grilling and broiling involves exposing the food to direct heat of a flame. Grilling usually denotes placing the items on a grill above the flame. Broiling is usually absent a grill as when the food is placed in an oven broiler where the flame is above.
If it’s boiling outside, then it’s hot enough for water to boil (figuratively). If it’s broiling, the heat of the sun above is broiling you like a London broil (almost literally).
Yes, that’s how I understand the terms (in cooking).
Sometime’s you say, I think, at the beach “the Sun is broiling hot,” which doesn’t really make sense.
So, Brits: sounds weird or not?
Or is Charley a Brit?
Weird. All is grilling in the UK. It was years before I figured out what broiling was. And yes, Charley is a Brit.
Yes. The word ‘broil’ simply doesn’t exist in our common vocabulary. Many people will have heard Americans say it (either in real life, or on TV or in films) - a fair number of Brits hearing the word ‘broil’ will just assume it’s a variant of ‘boil’.
Eye of round does really well using the slow-roasting method for roast beef. I mean, it’s not mouth buttery but it’s good. Better than you’de think, really.
You salt it well all over, rub on some pepper and herbs, wrap it in saran wrap, and let it sit 24-48 hours in the fridge.
Unwrap it, rinse off the salt, pat dry, reapply herbs, sear sides for brownness.
Place on roasting rack, roast at 225F until a thermometer registers 115 for medium rare (approx 1.5 hrs for 4 lb roast). I do not advise roasting it well done. And you can’t roast this cut by any high heat method. It will contract and turn inedible.