Bidding war for rental property - is this normal now?

Me and a few people are planning to move into a place in East London. We've been searching for a while, and have quite a few specific requirements we'd. We found somewhere that fulfills these, we love it and it's only been on the market for 1 day - due to Covid, there are nice places on the market for months on end at the moment. The agent knows we're keen, and has played on it a bit - told us that another other group are keen and we should get offers in quickly, sent me the offer forms as soon as he back to the office etc.

We put in an offer of the asking price, and the agent is now trying to ensue us in a bidding war, asking for 'best and final offers', saying the other group have also put in an offer today. I do think there's a decent chance the agent is simply lying about this.

Out of principle, we're refusing to raise our offer - surely the place should go to whoever put their offer in first, or whoever the landlord thinks is a 'better' tenant? Of course, this is normal practice when buying a house -but is this now normal when renting?

UPDATE: He wasn't bullshitting and the other group offered £100 above asking price. Quite surprised to see this happening in COVID times but it is what it is.