Accidental trackpad touches interfering with typing?

Years ago, using the keyboard on my old MacBook Pro would automatically disable the trackpad. It worked like a dream as the moment you stopped typing you could use the trackpad again.

Recently I had a new MacBook Pro from my work. I really thought something was wrong with it because I'd be typing away and suddenly the cursor would jump somewhere else and my text would appear in the wrong place. Then I bought another new MacBook Pro for personal use as my job came to an end and I had to hand the first one back - and I came to realise it was preference related rather than a fault because I had exactly the same issue on the new machine. Yet there is nothing in any of the preferences about preventing accidental trackpad touches while typing.

Please tell me I've missed something? I am starting to type with my wrists in the air, which is a strain and likely to bring on RSI. I really don't want to have to get an external keyboard out every time I type as having to use a second keyboard would negate the whole purpose of having an untethered laptop!