Potential blockage in rainwater downpipe possibly causing a leak above the front bedroom bay window?

Sometimes when it rains water leaks into the main bedroom. See photo below.

I recently had the gutters cleared but the problem is still ongoing.

No issues were mentioned regarding the condition of the gutters.

I have been told the roof tiles are fine. There is no moss on them.

There is no bathroom/shower room or any water storage or water pipework in the loft.

Could there be a partial blockage in the downpipe (perhaps in the double angle section near the top) as there are no cracks on the front of the house above the wooden windows and there is a soffit overhang over the bay window?

What should I use to clean/fully clear the inside of the downpipe:

1) Drain rods like: Rothenberger 130080 Universal Rods amazon.co.uk/Rot…M9I

Are any specific additional attachments required or worth purchasing?

2) Purchase a pressure washer with drain pipe hose attachment?

Any suggestions regarding required power, flow and a reliable one etc?

3) Something else?

I don't particularly fancy climbing up a telescopic ladder to the gutter level (in dry weather obviously) at present; so would rather do something from ground level to resolve the issue.

There seems to be a water stain on the painted ceiling next to the curtain rail.

What else could be causing the leak? I am otherwise stumped if it isn't an issue with the downpipe. I had hoped the gutter cleaning would have resolved the issue!

Currently I have been using a long flower pot to catch any drips.

Thanks for your help.