Don’t be too focused on being outbid. Bids are pretty much meaningless. What’s more relevant is a buyers position. Vendors would rather go for a lower proceedable offer than a higher pie in the sky bid.
The best thing you can do is get all your figures, house sale and paperwork in order and introduce yourself to the agents as a serious contender who knows what they’re doing and where they’re at. If you’re seriously in the running they won’t let you get out bid, they will want to get the vendor a sale at best possible price even if that means trying to get you into a bidding war.
A lot of agents won’t really want to engage with you until you at least get your sale well under way and can provide evidence of this, it sounds like there are months to go with your uncle purchasing, solicitor etc, so tell him to get a move on