I'm glad that people have already pointed out what I was going to- exercises like Uncleftish Beholding are ones in linguistic purism, are often a counterreaction to the older notion that latinate or hellenic root words are more prestigious, and are based on the equally silly notion that English would be far better off removing everything but Germanic-derived words from it.
As people have very sensibly pointed out, Old English already had quite a number of Latin loan words, many deriving from a Christian context but not all of them by any means. Whilst obviously the corpus of Old English has limitations, people do still generally feel able to date the presence of a particular Latin loan's appearance in Old English, and the collated data on that indicates that the number of loans over time gradually increased and accelerated. It seems to me ludicrous to imagine that an Old English without Norman would at best stop taking in Latin or Greek loanwords, and most preposterously purge itself of all of the pre-existing ones.
You would have thought that Old or Middle French loanwords would still, to some degree, have made their way into this theoretical *English, or at the very least some dialects. Likewise, unless we're butterflying away a perceived Renaissance, be that the 12th century variety or the one which often gets the definite article, the prominence of Latin and Greek is certainly going to intellectually increase in *English speaking societies in Britain. You may still very well end up with *English having specific loans coming from Classical philology, the equivalents of the real examples like 'medize/medise', 'cornucopia', 'cohort', 'aboriginal', 'metropolis' etc.
I've actually got a partially worked-out example of a non-Norman *English, but I, errr, call it Manglo-Saxon in a kind of self deprecatory instinct... It's also not got the most fidelity to what such a thing would really look like, because I have occasionally kowtowed to the simplicity of having some things coincidentally seem more like modern English. Having said that, do bear in mind that the pattern for most languages over time has generally been simplification, and the gradual loss of at least some final sounds regardless of the continued use of older orthography. Any attempt at *English should recognise that at least some form of simplification is likely, and that not all of the changes from Old to Middle English result from the influence of Anglo-Norman.