PhD Internship in smaller lab [D]

How much of a disadvantage is it if your only internship is not at one of the big frontier labs when it comes to post-phd opportunities in robotics/ML? My PhD is at a top university (UK) and my internship is interesting and relevant but the team itself is smaller and it's no Nvidia/Google/etc. Most places here prefer interns for 6 months so I'm not sure if I can do another internship down the line or if there's even much point compared to just wrapping up the PhD and then getting a job.

Is having a relevant internship already a big plus when it comes to applying to industry, or does it need to be a really well known big tech company?