Most of us will be knowing a few thousands of English words and there may be a few hundred this side or that. This is an average count. The count may increase if one takes into account the tenses, gerands, plurals, prefixes and suffixes.
Knowing the more words does not mean that we use all of them in our writings. In fact we manage with the minimum lot while writing because many difficult words we know require some more practice and knowledge of language if we really want to include them.
As regards to the counting of the words, the primitive method of telephone directory can be adopted which I followed when I wanted to know how many Sanskrit words I knew and to avoid duplication in counting I started to write them in a telephone directory mode by taking a big diary and allotting a few pages sequentially for the starting letters of the words in Devnagari or Hindi script.
In this case, one has to write English letters and give 5-6 pages for each letter and may be only 1-2 pages for j, q, v, x, y and z.
It is a long process and just scribble down the words coming in mind or seeing them written somewhere. Slowly it will grow into a compendium where before entering a new word we have to check whether it already exists there.
This method is not for every one. It is for those patient people who can give a few minutes daily to give to this activity and after a few years find the result.
A long method, that is why I called it as primitive one.
Knowledge is power.