Often they need 12 months history of charge card usage.... sometimes £200k household income is sufficient.... sometimes only £100k spend will suffice and other times more than £150k. But those conditions sound about right in general. To be safe, personally earn £300k p.a., spend £150k steadily in 12 months and have a Plat card with perfect payment history for 3 years lol.

Non-mentioned ones include a top-end Experian credit score (so make sure your billing address is your home address where you are registered for council tax and you haven't missed mortgage payments/other card payments), frequent use of Amex services (eg. PTS, concierge, telling them when you are abroad, secondary cards etc.), steadily increasing expenditure (likeliness it will go up from just £120k p.a.) and generally if they are in the mood for giving out invitiations (there was a hiatus for 2-3 years until 9 months ago).

If you meet general requirements as stated above, you may get through to a cent prospects group who probably contact you to discuss, tell about services, make sure you're happy with £1800 fee and do the basic credit score/Amex account checks (see how much and what you are are spending on). If they say OK, then it goes to new cent accounts who do the more serious checks (identity, income level, existing current account banking relationship) to see if Amex as a bank is willing to give you such a high-limit account in general. If they say OK, then you are in and you'll have the card in 10 days. Note there may be other "executive" level decisions in the above process as well somewhere, who knows.

I suspect as times goes on and Amex wants to retain the Cent's marketing strength that the ave Cent holder has £Xm in Net Worth, £Yk in disposable income and spends £Zk on holiday travel, that the requirements will slowly but surely change, and like the US, it will become strictly invitation only again. Don't want too many punters on £200k/year who personally spend £20k/year but run £100k expenses on raw material orders - good income for Amex, but perhaps not the discretionary spender they might be looking for (not that I personally have anything against people who do that!).