Could the Royal Navy have launched K3 battlecruisers before Washington?

If Britain had pursued the K3 design in 1920, could it have launched mostly completed ships before the Washington Treaty?

Yes, Britain had the industrial capacity, although the larger challenge was maintaining and upgrading the worldwide infrastructure such ships required.

British construction capacity cannot be judged from domestic dry docks alone because an imperial navy had to maintain facilities across many stations. Deferring incremental upgrades through the First World War made subsequent modernization much more expensive and politically harder to fund. British yards could drive a K3 program hard enough to have ships substantially advanced before Washington. The longer-term penalty would be enlarging docks and support facilities throughout an empire whose global bases were both a strategic advantage and a recurring maintenance liability.