From Gov.uk:

"Up to 28 April 2021, the MHRA had received Yellow Card reports of 242 cases of major thromboembolic events (blood clots) with concurrent thrombocytopenia (low platelet counts) in the UK following vaccination with COVID-19 Vaccine AstraZeneca. These events occurred in 141 women and 100 men aged from 18 to 93 years and the overall case fatality rate was 20% with 49 deaths. Six cases have been reported after a second dose .

Cerebral venous sinus thrombosis was reported in 93 cases (average age 47 years) and 149 had other major thromboembolic events (average age 55 years) with concurrent thrombocytopenia.

The estimated number of first doses of COVID-19 Vaccine AstraZeneca administered in the UK by 28 April was 22.6 million and the estimated number of second doses was 5.9 million."

So about a 1 in a million chance of blood clots with low platelets after a second dose.