Jalima When I see my friend, I'll ask her about the nationality of her co-workers. I could be wrong and will eat humble pie, but I know she's worked there for years and is definitely British. She's talked about her work sometimes and I've never had the impression that many of them are non-British. I know they have to be able to speak at least two languages. British workers tend to be underepresented in EU admin jobs, because there's a shortage of British polyglots.
Even the sainted Guardian isn't beyond fake news! 
The horse's mouth doesn't say anything about the nationality of the temporary or contract agents,some of whom some are probable British.
I know there's a difference between jobs and staff, which is why I mentioned it as an additional point. There are two issues: unemployment and loss of taxes paid to the Treasury.
There are other issues, too, such as the delay in the UK getting approval for medicines, the cost of which which will have to be paid to outside regulatory authorities and the loss of pharma jobs, which gravitate to the UK, partly because the EMA is here.
Anyway, I'll ask my friend next time I see her. She's not too bothered personally, because she's in her late fifties and will receive a huge redundancy package courtesy of the British taxpayer, as part of the multi-billion divorce settlement. I suppose she could always pick cabbages for pocket money. It's the country's loss.