Firstly you don’t have a connecting flight as it’s a separate ticket.
Secondly the answer is it depends how benevolent QR, They MIGHT rebook you free, for a fee or fare difference or they could tell you sorry you didn’t check in on time itinerary is cancelled.
Whilst 6 hours on the grand scheme of things seems reasonable it’s one of the worst options. LCY is prone to a lot of early morning fog/weather cancellations. If BA we’re to cancel your flight theat 6 hrs is nothing is you need to schlep it to Gatwick, Heathrow or Luton/Stanstead for an alternative flight.
You could fly the day before does give you more options but still a lot of stress trying to get to AMS.n
I know this is Flyertalk but I’d personally take the overnight Stena Line ferry. Leave Liverpool Street at 1930 the previous evening. Train direct to Harwich International. Few steps to check in. Minimum security ie all luggage through X-ray machine to liquids out or shoes off. Board the ferry and find your well appointment en suite cabin .
id then have a leisurely dinner with a nice wine in the Ala Carte Restaurant, a drink or two at the bar then retire to bed.
Cabins are quipped with TV and as has been pointed out the camera viewing the pets kennels is magical to watch the animals in the night and joyous when they are reunited with their owners in the morning.
Id then have a nice powerful shower around 6am local time after up to 8 hours sleep. If I was inclined I’d go for breakfast which can be anything from an unlimited buffet to a croissant, juice and coffee. At 8am I’d walk to the metro station outside the door of Hoek Van Holland Station for the journey to Rotterdam where I’d change for the train up to Schipol where I’d arrive refreshed and relaxed at 10am local time.
A through ticket from London to Hook of Holland is around £100 including cabin. Meals on top and post covid you can no longer get a ticket all the way to any Dutch Station so you need to buy the metro/train ticket separately but I’d say for around £150 you’ve had a very sophisticated comfortable journey. I’ve never known a ship to be cancelled as they can operate in rough seas. The crossing can be done in around 6hrs but the ship slows down so you don’t arrive at stupid o’clock. That way IF it’s delayed leaving theUK it can go faster .
I guess the only you know the importance of QR not budging. Way too risky for me.. if it was a a £200 city break I’d take it on the chin but I’d happily spend £150+ to arrive stress free.