1 hour enough time to make connecting flight at Heathrow?

If you aren't changing terminals on a proper connection it is tight but not impossible. You don't have to go though customs and immigration but will go through security.

Thanks for the info and quick response Marco!

We have gone through Heathrow a couple of times and 70 minutes is possible, but I always try to book two hours for transferring from International to within Europe. This is true for Amsterdam and Paris DeGaule as well.

I wouldn't want to risk it - even without changing airlines.

You could end up behind really stupid people in the security line and lose a lot of time. If you're flying in business you will have access to the "Admiral's Club" of whatever airline you're flying and a longer wait won't be so bad.

My travel plans always take into account my personal level of paranoia.

You will not go through immigration or customs in London. You will go through a security screen (and they will check your ticket/id). You will stay airside and follow the signs for flight connections.

I have made flights with short connections like this; you need to be prepared to hustle to your next flight. I have also missed longer connections at Heathrow on two occasions. In both cases, my flight from the U.S. was significantly delayed and I knew I had missed my connection before the plane even landed. In both cases, the airline put me on a flight a couple hours later.

Factors to consider:
Is this one ticket? Are there later flights to Budapest? Is the airline a European carrier? Are you traveling at a particularly busy time like a holiday weekend? How upset would you be if you got stuck in London for an extra day? Do you get stressed rushing through airports?

I often choose short connections because I hate sitting around in airports ... but I am comfortable with rushing to my gate and taking the risk that I will be delayed.

To see exactly what's involved in changing planes at Heathrow, go to their Flight Connections Planner website and put in all your details: https://www.heathrow.com/flight-connections

I'm looking to book a business class ticket that makes a connection in
Heathrow.. It's an international flight from Phx AZ. to Budapest. I
was wondering if one hour is enough time to make my connecting flight
to Budapest? (it's actually 70 mins...) Not changing airline, just
planes.... I think we'll need to go through customs in London so I'm
concerned that 1 hour isn't enough time. thank you in advance!

If you miss that connecting flight (this is one itinerary?) due to your inbound being late for example, how many flights are there to Budapest for the rest of the day? Remember, if you miss your connection, the airline can only put you on subsequent flights that have seats available. That could mean spending the night at Heathrow.

Last, don't check any luggage. The chances of your checked luggage getting on the 2nd flight are shaky.

Travelling business will entitle you to the fast track security lane(s). Whilst not necessarily avoiding 'the stupid' it probably will help.

Do check on arrival in which part of the terminal you have landed and when your departure is as it may be possible to short-circuit the transit distance.

If you arrive at 5A or depart from 5A you have to go through the central security.
If you arrive at 5B or 5C and depart from 5B or 5C you do not need to go to the centre but can clear security at the satellite. This can save a good 20 minutes.

Unfortunately this varies from day to day. The long-haul flights tend to use the B and C satellites, but the intra-Europe flights can be anywhere.

Do you know for sure that both flights are in Terminal 5?

They are the only flights with the same airline connecting at Heathrow on this through route, presuming the OP hasn't been confused by codeshare.

Is your plan BA 288 connecting to BA 868?

BA shows 70 minutes.

You will likely be 'on the move' the entire time, so do not plan to stop for a snack. Your biz class privilege to use 'fast lanes' will help

Be sure you have your boarding pass for the 2nd flight to keep things moving along

EDIT-- Using the link Harold provided and picking a random date in April it shows both flights using Terminal 3. What it may be on your travel dates could be different.

thanks for all the help! the flight calculator does show 70 mins required so I guess I'll take the chance. There are a few more flights out that day so if we have to take a different flight we can, and I'm OK spending time in Heathrow.

I had checked through the connections tool and thought a terminal 5-5 transfer had come up, but doing it again on another random date it came up as 3-3. Either it does change sometime or I simply misread it somehow the first time.

Advice for a 3-3 transfer is to be prepared for some long walks as some gates are 20 minutes walk from the central area.