Even though it's a few years old now I second Hugh Fearnley Whittingstall's River Cottage Veg Every Day! as one of my favourites. I've also got quite a bit of use out of River Cottage Light & Easy.
Along a similar vein there are the Nigel Slater Greenfeast books, one for Spring-Summer, another for Autumn-Winter.
Anna Jones - A Modern Way To Eat/A Modern Way to Cook/The Modern Cook's Year are also great books - probably a little trendier in terms of ingredients etc. Quite a few of her recipes are on the guardian website to give you an idea.
There are the Leon books as well e.g. Leon Fast Vegetarian and Fast Vegan - these are lovely books
Rose Elliot - New Complete Vegetarian is more old-fashioned but I have used it quite a bit for dependable family recipes.
Meera Sodha's "Fresh India" is a mix of easier and more time-consuming Indian dishes. I don't have Meera Sodha's "East" but it's on my wishlist.
My wildcard suggestion is The Easy Vegetarian Kitchen by Erin Alderson (blogger Naturally Ella) which takes a base meal such as "mac and cheese" and then suggests seasonal variations. I love this book on a personal level but it isn't a well known one!
Some of my favourites for vegan options:
Thug Kitchen - I love this one but there is a lot of bad language which may be a dealbreaker for some! I have successfully gifted this one to a young vegetarian couple before.
Vegan Street Food by Jackie Kearney (South-East Asian and vegan)
Aine Carlin - Keep It Vegan
the Bosh! series. I suspect the Speedy Bosh book is the most family friendly but this is the one that I don't have.
When I'm looking for something quick and easy I often have a look at Katy Beskow's books (e.g. 15-minute vegan) or Robin Robsertson (e.g. Quick-Fix Vegan) but I personally don't think they're quite as nice for gifts.
I have the Susie Middleton books and they're lovely but I never reach for them - I'll have to have give them another try based on the recommendations here.
Good luck!