How easily you can get by in Europe depends very much on country. Broadly speaking, I find that Western and Northern Europe are very English friendly, and Eastern Europe (e.g. former Soviet countries) are not. The following is based on my experiences in various countries, YMMV:
Netherlands, Denmark, and Sweden: almost everyone speaks near perfect English, there is absolutely no problem at all conducting your business in English. In Copenhagen, people are (mildly) offended if you even ask if they speak English. So just open in English, and if they speak to you in Danish apologise and say you only speak English. However, whilst everyone speaks English: signs, menus, and attractions (e.g. museums, etc.) are often only in the local language outside of tourist spots.
Germany, Switzerland and Austria: heavily dependent on where you are. In Hamburg, Vienna, Cologne, Zurich or Berlin you will have no problem speaking English; however if you go into more rural locations you're much more likely to encounter shop staff, hotel staff, waiters, etc. who do not understand English or are uncomfortable speaking it with you.
France: much more English friendly than it used to be, and the famous French hostility to English speakers seems to have diminished. I've noticed a huge difference in ski-resorts, in particular. Still, even in tourist spots in Paris you'll encounter people who will not interact with you in English. However, if you know a handful of French words and are friendly you'll usually get by fine.
Czech, Hungary, Croatia, Slovenia, Slovakia: outside of the biggest cities and most touristy spots (e.g. you'll be fine in Prague), English friendly places are uncommon. However, we found almost all tourist facing people spoke enough German to get by.
I haven't spent enough time in Luxembourg or Belgium to form a view, since I've only ever stopped for lunch or fuel there, but the people we encountered spoke English so I think it's probably fine.
I invite others to edit to add countries I haven't covered (since I have no experience of them) here
Southern Europe (Spain, Portugal, Italy) is so-so. You can get by in larger cities but in the boonies and smaller cities it's hit or miss even with younger people. (Copied from comment by @hilmar)