Speakers Corner is just that - a place where speakers can go and spew forth on whatever they wish with the proviso that what they say must not be incitement to violence in relation to race, creed, colour, sexual orientation etc., or insurrection /sedition. Proscribed organisations may not use the facility and neither may their philosophy be spoken by individuals.
At Speakers' Corner, speakers have to put up with whatever verbal abuse is aimed at them - if they can't then it's best not to be there! That is why it is called Speakers' Corner. Physical abuse is not tolerated by the authorities. The policy is that we have the right to free speech in the UK, with the caveats mentioned being enforced, and Speakers' Corner maintains that right.
There is no law in the UK against praying on the street provided you are not cauisng an obstruction to the lawful use of that area by other people. Muslims have used sections of roads before for outdoor services, in the UK, for which a licence has been granted, in much the same way that Christians can, as also other faith groups, or secular groups. Christian groups when working outside sometimes have people on the perimeter of the group to ensure that other people can pass by (ie so that they are in the area covered by the licence granted them). Provided all groups remain with the law and the teaching is not an incitement to violence in relation to race, creed colour, sexual orientation, or insurrection / sedition it is lawful.
In all such cases if violence is seen the authorities will either maintain order or, as a last result, will simply close down the meeting / prayers, whatever. Groups that have a record of violence surrounding them, because of their message, are unlikely to gain a licence in the future. Licences are granted by the local Council and relate to one 'event' - blanket licences do not exist; Speakers' Corner is an (probably, only) exception. Violence does happen at meetings sometimes - it would be a fool who says it doesn't happen - but it is dealt with and the perpetrators are taken to court, using official CCTV where necessary.
That is why I said I am glad I am English! We have simple laws that apply to all, and will be enforced against all, if necessary. It realy confuses me when I look at the UK and America see how the Americans attack the UK all the time on here. Many (most) US citizens see the UK as being a mini-USA, in both government and lifestyle. May it never, ever, be! We are not! We are not perfect, but we value simple freedoms, which is why Brexit was so popular and gives us, again, the right to self determination as a country, and no longer subservient to an increasingly invasive big brother.