The high tax rates of the mid to late 1970s may have spawned the tax avoidance industry through companies like Rossminster, but avoidance by the wealthy was around for decades before then. For example the Duke of Westminster, or the egregious activities of the Vesty family.
But as Income Tax rates, particularly for the wealthy, fell with Thatcher and subsequent governments, avoidance didn't fall, it grew. That growth was fuelled not by tax rates, but by companies earning large sums of money from devising schemes which could be mass marketed to all groups of earners; from multimillionaire business owners to factory workers. Neither was it restricted to Income Tax. VAT, Corporation Tax, National Insurance, CGT and Stamp Duty were all attacked.
What has changed is;
a) Governments being more proactive in tackling avoidance, whether this be with the introduction of broader legislation such as the Disclosure of Tax Avoidance Scheme (DOTAS), or the introduction of specific legislation to block loopholes that were being exploited.
b) The Court's view of the transactions which form the avoidance schemes.